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Geometry Group
Members
Projects
Lehre
Seminare
Archive
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Preceding Projects
The project "Geometric Problems and Special PDEs" continues two projects: "PDEs and Submanifolds"
and "Integrable
Systeme in der Differentialgeometrie" of SFB 288.
Topics
It is a central topic of this project to find solutions for certain types of partial differential equations (PDEs) via the geometric context in which they arise. Typical examples are highly complicated, nonlinear fourth order PDEs which appear when studying curvature problems in affine hypersurface theory, e.g. so called affine Bernstein type problems. In cooperation with Chinese partners, we made significant progress during recent years. A monograph with one author from the TU Berlin and three authors from the geometry school at Sichuan U will appear in 2010 (World Scientific).
Vice versa, the geometry of certain types of submanifolds in different spaces can be investigated and classified via the solution of PDEs, e.g. in the conformal geometry of surfaces or for different types of submanifolds. It is the aim of the projects to investigate the following:
- Variational problems and higher order PDEs,
- Projectively flat manifolds and generalized spherical harmonics,
- Submanifolds,
- Conformal geometry of surfaces,
- Curvature operators of conformal and projective type,
applications to submanifolds,
- Discrete differential geometry and visualization.
The list of recent publications below indicates the progress that we made in cooperation with our project partners. Our research activities have been stimulated by research visits, workshops and conferences; they are of particular importance for the promotion of young scientists. The following and the homepages of the foregoing projects document our activities and international cooperations over many years, in particular a strong cooperation with excellent Chinese geometers during the last two decades. Additionally to the support by DFG and NSFC our German-Chinese cooperation has been co-financed by TU Berlin (International Office), Alexander von Humboldt-Stiftung and and Dierks von Zweck-Stiftung (Essen), our cooperation with East-European countries by TU Berlin (International Office) and Dierks von Zweck-Stiftung.
Conferences
- 2011, Conference in Beijing, China.
- 2010, October, Workshop in Beijing, China.
- 2009, September 05-10, 9th Internat. Conf. Geometry Appl., Varna/BG
- 2009, July, Selected Topics in Discrete Differential Geometry and Visualization, Peking University, China
- 2008, September, Workshops Beijing and Kunming (China)
- 2008, 23.06. - 27.06., Differential Geometry Conference, Banach Center Bedlewo/PL
- 2007, 03.09. - 09.09., 8th Internat. Conf. Geometry Appl., Varna/BG
- 2007, 03.07. - 07.07., Symposium on the differential geometry of Submanifolds, U Valenciennes (F)
- 2007, 10.04. - 13.04., Int. Congress Pure Applied Diff. Geom., KU Brussel/EHSAL, B.
- 2006, 03.09., Workshop on Affine Diff. Geom. and Information Geometry, Sichuan Univ. Chengdu, China.
- 2006, 1.10. - 7.10., Geometrie-Tagung, Oberwolfach
- 2005, 26.9. - 30.9., Differential Geometry Conference, Banach Center Bedlewo (Poland).
- 2005, 04.9. - 10.9., 7th Internat. Conf. Geometry Appl., Varna/BG
- 2005, 16.-24.8., Workshop Conformal Geometry, Beijing and Chengdu, China.
- 2004, 26.9. - 02.10., Geometrie-Tagung, Oberwolfach.
- 2003, 23.9. - 27.9., PDEs, Submanifolds and Affine Differential Geometry , Banach Center Bedlewo (Poland).
Foregoing conferences, workshops and events
Cooperating mathematicians from China
- Beijing, Peking University (Beida):
- Wang Changping, Ma Xiaonan, Ma Xiang, Fan L.
- Beijing, Tsinghua University:
- Li Haizhong, Wang Xianfeng, Ma Hui.
- Chengdu, Sichuan University:
- Li An-Min, Chen Bohui, Jia Fang, Wang Baofu, Zhao Guosong.
- Administrators: Ms. Zeng Ling, Ms. Li Ting, Ms. Liu Ying
- Kunming, Yunnan Normal University:
- Guo Zhen
- Shanghai, East China Normal University:
- Lin Limiao
- Shanghai, Fudan University:
- Xin Yuanlong
- Shenyang, Northeastern University:
- Liu Huili
- Zhengzhou, Zhengzhou University:
- Hu Zejun
- Xinxiang, Henan Normal University:
- Xu Ruiwei
- Hangzhou, Zhejiang University:
- Shen Yibing
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Guests 2010
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Name | Origin | Period |
Tian, Haoshu |
Peking University, Beijing, China |
15.01. - 17.02.10 |
Jin, Wei |
Peking University, Beijing, China |
15.01. - 17.02.10 |
Carriazo, Alfonso |
Universidad de Sevilla, Spain |
14.06. - 20.06.10 |
García-Río, Eduardo |
Universidade de Santiago de Compostela, Spain |
15.06. - 30.06.10 |
Opozda, Barbara |
Instytut Matematyki UJ, Krakow, Poland |
01.07. - 31.07.10 |
Nikcevic-Simic, Stana |
University of Belgrade, Belgrade, Serbia |
20.07. - 26.08.10 |
Gilkey, Peter |
U Oregon, Eugene, USA |
11.08. - 26.08.10 |
Matsuzoe, Hiroshi |
Nagoya Institute of Technology, Japan |
01.09. - 04.09.10 |
Encheva, R. |
U Shumen, Bulgaria |
17.09. - 30.09.10 |
Georgiev, G. |
U Shumen, Bulgaria |
17.09. - 30.09.10 |
Borisenko, A. |
Kharkov State U, Ukraina |
01.10. - 31.10.10 |
Deszcz, R. |
U Life Sc. Wroclaw |
29.10. - 20.11.10 |
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Guests 2009
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Name | Origin | Period |
Vrancken, Luc |
Université de Valenciennes, France |
20.02. - 22.02.09 |
Xu, Ruiwei |
Henan Normal University, Xinxiang, China |
01.06. - 31.07.09 |
Zeng, Ling |
Sichuan University, Chengdu, China |
01.06. - 31.07.09 |
Nikcevic, Stana |
University of Belgrade, Belgrade, Serbia |
02.08. - 14.09.09 |
Gilkey, Peter |
U Oregon, Eugene, USA |
17.08. - 28.08.09 |
Opozda, Barbara |
Instytut Matematyki UJ, Krakow, Poland |
22.09. - 26.10.09 |
Deszcz, Ryszard |
Wroclaw University of Environmental and Life Sciences, Wroclaw, Poland |
29.10. - 19.11.09 |
Nikcevic, Stana |
University of Belgrade, Belgrade, Serbia |
10.11. - 30.11.09 |
Oliker, Vladimir |
Emory University, Atlanta, Georgia, USA |
21.11. - 31.12.09 |
Lin, Limiao |
East China Normal University, Shanghai, China |
21.11. - 31.12.09 |
Vrancken, Luc |
Université de Valenciennes, France |
18.12. - 20.12.09 |
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Guests 2008
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Name | Origin | Period |
Opozda, Barbara |
Instytut Matematyki UJ, Krakow, Poland |
01.05.-15.05.08 |
Nikcevic, Stana |
University of Belgrade, Belgrade, Serbia |
14.05.-13.06.08 |
Li, An-Min |
Sichuan University, Chengdu, China |
01.06.-31.07.08 |
Xu, Ruiwei |
Sichuan University, Chengdu, China |
01.06.-31.07.08 |
Stanilov-Ivanov, G. |
Sofia University St. Kliment Ohridski, Sofia, Bulgaria |
09.06.-22.06.08 |
Oliker, Vladimir |
Emory University, Atlanta, Georgia |
17.06.-13.07.08 |
Nishikawa, Seiki |
Tôhoku University, Sendai, Japan |
21.06.-22.06.08 |
Vrancken, Luc |
Université de Valenciennes, Valenciennes, France |
30.07.-12.08.08 |
Mihai, A. |
University of Bukarest, Bukarest, Rumania |
13.08.-23.08.08 |
Mihai, I. |
University of Bukarest, Bukarest, Rumania |
13.08.-23.08.08 |
Hasegawa, K. |
University of Tokyo, Tokyo, Japan |
25.08.-22.09.08 |
Deszcz, Ryszard |
Wroclaw University of Environmental and Life Sciences, Wroclaw, Poland |
29.10.-14.11.08 |
Opozda, Barbara |
Instytut Matematyki UJ, Krakow, Poland |
15.11.-14.12.08 |
Nikcevic, Stana |
University of Belgrade, Belgrade, Serbia |
01.12.-15.12.08 |
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Guests 2007
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Name | Origin | Period |
Opozda, Barbara |
Instytut Matematyki UJ, Krakow, Poland |
27.01.-10.02.07 |
Vrancken, Luc |
Université de Valenciennes, Valenciennes, France |
24.02.-04.03.07 |
Stanilov, Grosio |
Sofia University, Sofia, Bulgaria |
25.03.-09.04.07 |
Oliker, Vladimir |
Emory University, Atlanta, Georgia |
23.05.-31.05.07 |
Hineva, Stefana |
Sofia University, Bulgaria |
03.06.-29.06.07 |
Encheva, Radostina |
Schumen University, Bulgaria |
14.06.-30.06.07 |
Georgiev, Georgi |
Schumen University, Bulgaria |
14.06.-30.06.07 |
Li, Haizhong |
Tsinghua University, Beijing, China |
01.07.-05.09.07 |
Wang, Changping |
Peking University, Beijing, China |
02.07.-31.07.07 |
Hu, Zejun |
Zhengzhou University, Zhengzhou, China |
01.08.-31.08.07 |
Gilkey, Peter |
University of Oregon, Eugene, Oregon, USA |
16.08.07 |
Vrancken, Luc |
Université de Valenciennes, Valenciennes, France |
18.08-21.08.07 |
Li, An-Min |
Sichuan University, Chengdu, China |
01.09.-30.09.07 |
Li, Ting |
Sichuan University, Chengdu, China |
01.09.-30.09.07 |
Chen, Bohui |
Sichuan University, Chengdu, China |
01.09.-30.09.07 |
Nikcevic, Stana |
University of Belgrade, Belgrade, Serbia |
12.09.-30.09.07 |
Viesel, Helmut |
TU Karlsruhe, Karlsruhe, Germany |
12.10.-16.10.07 |
Opozda, Barbara |
Instytut Matematyki UJ, Krakow, Poland |
15.09.-13.10.07 |
Nishikawa, Seiki |
Tôhoku University, Sendai, Japan |
15.10.-28.10.07 |
Deszcz, Ryszard |
Wroclaw University of Environmental and Life Sciences, Wroclaw, Poland |
30.10.-29.11.07 |
Nikcevic, Stana |
University of Belgrade, Belgrade, Serbia |
01.12.-20.12.07 |
Mihai, A. |
University of Bukarest, Bukarest, Rumania |
14.12.-22.12.07 |
Mihai, I. |
University of Bukarest, Bukarest, Rumania |
14.12.-22.12.07 |
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Guests 2006
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Name | Origin | Period |
Hu, Zejun |
Zhengzhou University, Zhengzhou, China |
01.01.-31.01.06 |
Dillen, Franki |
Katholieke Universiteit Leuven, Leuven, Belgium |
08.02.-12.02.06 |
Nikcevic, Stana |
University of Belgrade, Belgrade, Serbia |
03.05.-31.05.06 |
Deszcz, Ryszard |
Agricultural University, Wroclaw, Poland |
07.05.-10.05.06 |
Vrancken, Luc |
Universite de Valenciennes, Valenciennes, France |
19.07.-03.08.06 |
Xin, Yuanlong |
Fudan University, China |
19.07.-21.07.06 |
Deszcz, Ryszard |
Agricultural University, Wroclaw, Poland |
29.10.-24.11.06 |
Gilkey, Peter |
University of Oregon, Eugene, Oregon, USA |
02.11.06 |
Brozos-Vazquez, M. |
University of Santiago de Compostela, Santiago de Compostela, Spain |
02.11.06 |
Vrancken, Luc |
Université de Valenciennes, Valenciennes, France |
10.11.-13.11.06 |
Verstraelen, Pol |
KU Leuven, Belgium |
15.11.-19.11.06 |
Ivanov, Stefan |
University Sofia, Bulgaria |
22.11.-20.12.06 |
Nikcevic, Stana |
University of Belgrade, Belgrade, Serbia |
25.11.06-31.12.06 |
Opozda, Barbara |
Instytut Matematyki UJ, Krakow, Poland |
01.12.-22.12.06 |
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Guests 2005
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Name | Origin | Period |
Opozda, Barbara |
Instytut Matematyki UJ, Krakow, Poland |
17.01.-03.02.05 21.08.-03.09.05 |
Wang, Changping |
Peking University, Beijing, China |
20.06.-20.07.05 |
Gilkey, Peter |
University of Oregon, Eugene, Oregon, USA |
01.07.-15.07.05 |
Hu, Zejun |
Zhengzhou University, Zhengzhou, China |
08.07.-31.01.06 |
Guo, Zhen |
Yunnan Normal University, Kunming, China |
01.08.-31.10.05 |
Li, An-Min |
Sichuan University, Chengdu, China |
01.08.-31.10.05 |
Vrancken, Luc |
Universite de Valenciennes, Valenciennes, France |
09.08.-24.08.05 09.12.-14.12.05 |
Stanilov, Grosio |
Sofia University, Sofia, Bulgaria |
17.09.-15.10.05 |
Oliker, Vladimir |
Emory University, Atlanta, Georgia |
23.09.-03.10.05 |
Brito, Fabiano |
Universidade de Sao Paulo, Sao Paulo, Brasil |
23.09.-02.10.05 |
Nikcevic, Stana |
University of Belgrade, Belgrad, Serbia and Montenegro |
30.09.-30.11.05 |
Reckziegel, Helmut |
Universität zu Köln, Köln, Germany |
21.10.-27.10.05 |
Nishikawa, Seiki |
Tôhoku University, Sendai, Japan |
22.10.-11.11.05 |
Deszcz, Ryszard |
Agricultural University, Wroclaw, Poland |
31.10.-13.11.05 28.11.-11.12.05 |
Hertrich-Jeromin, Udo |
University of Bath, Bath, United Kingdom |
12.12.-31.12.05 |
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Guests 2004
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Name | Origin | Period |
Opozda, Barbara |
Instytut Matematyki UJ, Krakow, Poland |
12.01.-23.01.04 01.12.-14.12.04 |
Vrancken, Luc |
Universite de Valenciennes, Valenciennes, France |
14.01.-16.01.04 27.04.-02.05.04 04.08.-23.08.04 |
Georgiev, Georgi |
Konstantin Preslavsky Univ., Shumen, Bulgaria |
01.09.-30.09.04 |
Deszcz, Ryszard |
Agricultural University, Wroclaw, Polen |
26.10.-07.11.04 28.11.-12.12.04 |
Nikcevic, Stana |
University of Belgrade, Belgrad, Serbia and Montenegro |
01.11.-30.11.04 |
Blazic, Novica |
University of Belgrade, Belgrad, Serbia and Montenegro |
01.11.-30.11.04 |
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Guests 1997-2003
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See the old homepage.
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Seminars
Doctoral Thesis / Habilitation Thesis
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C. Bohle,
Möbius Invariant Flows of Tori in S4,
doctoral thesis, TU-Berlin (2003).
-
B. Springborn,
Variational principles for circle patterns,
doctoral thesis, Fac. II, TU Berlin (2003).
-
G. P. Peters,
Soliton Spheres,
doctoral thesis, TU-Berlin (2004).
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X. Ma,
Willmore surfaces in Sn: transforms and vanishing theorems,
doctoral thesis, TU-Berlin (2005).
-
M. Schmies,
Computational Methods for Riemann Surfaces and Helicoids with Handles,
doctoral thesis, TU Berlin (2005).
-
M. Wiehe,
Invariants in Affine Differential Geometry,
habilitation thesis, TU-Berlin (2005).
-
C. Scharlach,
Affine Geometry of Surfaces and Hypersurfaces in R4,
habilitation, Fac. II, TU Berlin (2006).
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M. Scherfner,
Kinematical Aspects of Lorentzian 4-Manifolds and Curvature of Submanifolds,
habilitation, Fac. II, TU Berlin (2006).
-
C. Bohle,
Constrained Willmore Tori in the 4-Sphere,
habilitation thesis, Fac. II, TU Berlin (2008).
-
B. Springborn,
Advances in the Discrete Differential Geometry of Surfaces,
habilitation, Fac. II, TU Berlin (2008).
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F.-F. Henrich,
Loop Spaces of Riemannian Manifolds,
doctoral thesis, Fac. II, TU Berlin (2009).
Since 1991, within our foregoing projects, we supervised 25 PhD
thesis and 6 habilitations.
Publications
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N. Abe, K. Hasegawa,
A Generalization of Cartan's Identities for Isoparametric Hypersurfaces and Its Applications,
Results Math. 52 (2008), 197-210.
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J. A. Aledo, A. Martínez and F. Milán,
Affine Maximal Surfaces with Singularities,
Results Math. 56 (2009), 91-107.
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T. Binder,
Relative Tchebychev hypersurfaces which are also translation hypersurfaces,
Hokkaido Math. J 38 (2009), 97-110.
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T. Binder,
Higher Order Derivatives Gravity Curves,
preprint (2008).
-
T. Binder, M. Wiehe,
Invariance Groups of Relative Normals,
Banach Center Publications 69 (2005), 171-178.
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N. Blazic, P. Gilkey, S. Nikčević, U. Simon,
The Spectral Geometry of the Weyl Conformal Tensor,
Banach Center Publications 69 (2005), 195-203.
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N. Blazic, P. Gilkey, S. Nikčević, and U. Simon,
Algebraic Theory of Affine Curvature Tensors,
Archivum mathematicum (Brno) 42 (2006), supplement, 147-168.
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C. Bohle,
Constant Mean Curvature Tori as Stationary Solutions to the Davey-Stewartson Equation,
preprint (2008), arXiv:0810.1238v1 [math.DG].
-
C. Bohle,
Constrained Willmore Tori in the 4--Sphere,
preprint (2008), arXiv:0803.0633v1 [math.DG].
-
C. Bohle, K. Leschke, F. Pedit, U. Pinkall,
Conformal Maps from a 2-Torus to the 4-Sphere,
preprint (2007), arXiv:0712.2311v1 [math.DG].
-
C. Bohle, F. Pedit, U. Pinkall,
Discrete Holomorphic Geometry I. Darboux Transformations and Spectral Curves,
Journal für die reine und angewandte Mathematik (Crelles Journal) 637 (2009), 99-139,
ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2009.092,
arXiv:0803.0716v1 [math.DG].
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C. Bohle, F. Pedit, U. Pinkall,
The Spectral Curve of a Quaternionic Holomorphic Line Bundle over a 2-Torus,
Manuscr. Math. 130 (2009), 311-352,
ISSN (Print) 0025-2611, ISSN (Online) 1432-1785, DOI: 10.1007/s00229-009-0288-x,
arXiv:0904.2475v1 [math.DG].
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C. Bohle, P. Peters,
Bryant Surfaces with Smooth Ends,
Comm. Anal. Geom., 17 (2009), no. 4, 587-619,
arXiv:math/0411480v3 [math.DG].
-
C. Bohle, P. Peters,
Soliton Spheres,
to appear in Trans. Amer. Math. Soc., arXiv:0905.2162v1 [math.DG].
-
C. Bohle, P. Peters, U. Pinkall,
Constrained Willmore Surfaces,
Calc. Var. Partial Differential Equations 32 (2008), 263-277, arXiv:math/0411479v3 [math.DG].
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N. Bokan, M. Djoric, U. Simon,
Geometric Structures as Determined by the Volume of Generalized Geodesic Balls,
Results Math. 43 (2003), no. 3-4, 205-234.
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S. Born, M.Kossowski, M. Scherfner,
Characteristic Classes for Pseudo Riemannian Minifolds with Volume-Resolvable Metric Singularities,
preprint (2009).
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M. Brozos-Vázquez, P. Gilkey, S. Nikčević, U. Simon,
Projectively Osserman Manifolds,
Publications Mathematicae (Debrecen) 72 (2008), 359-370.
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M. Brozos-Vázquez, P. Gilkey, S. Nikčević, R. Vázquez-Lorenzo,
Geometric Realizations of Para-Hermitian Curvature Models,
Results Math 56 (2009), 319-333.
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F. E. Burstall, D. Ferus, K. Leschke, F. Pedit, U. Pinkall,
Conformal Geometry of Surfaces in S4 and Quaternions,
Lecture Notes in Mathematics 1772 (2002), Springer-Verlag, Berlin.
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F. E. Burstall, F. Pedit, U. Pinkall,
Schwarzian Derivatives and Flows of Surfaces,
in Differential Geometry and Integrable Systems, eds. M.A. Guest, R. Miyaoka and Y. Ohnita, Contemporary Math., Amer. Math. Soc. (2002).
-
S. C. de Almeida, F. G. B. Brito, R. Nozaki,
Closed Special Weingarten Surfaces in the Standard Three Sphere,
Results Math 56 (2009), 501-518.
-
R. Deszcz, M. Plaue, M. Scherfner,
On a Particular Class of Generalized Static Spacetimes
to appear in J. Geom. Phys. (2009).
-
R. Deszcz, M. Scherfner,
On a Particular Class of Warped Products with Fibres Locally Isometric to Generalized Cartan Hypersurfaces,
Colloq. Math. 109 (2007), 13 - 29.
-
F. Dillen, T. Lusala, M. Scherfner, G. Verbouwe,
Characterization of Quadrics by the Principal Curvature Functions,
Arch. Math. 81 (2003), 342 - 347.
-
F. Dillen, U. Simon, L. Vrancken (eds.),
Symposium on the Differential Geometry of Submanifolds,
Lab. Math. Appl. Univ. Valenciennes, 2007, ISBN: 978-1-8479-9016-7
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F. Dillen, G. Verbouwe,
Divisibility of the Second Fundamental Form of Hypersurfaces of Space Forms,
Results Math. 52 (2008), 247-260.
-
A. Dirmeier, M. Plaue, M. Scherfner,
On Conformal Vector Fields Parallel to the Observer Field,
Adv. Lorentz. Geom. (2008).
-
R. P. Encheva, G. H. Georgiev,
Similar Frenet Curves,
Results Math 55 (2009), 359-372.
-
D. Ferus, K. Leschke, F. Pedit, U. Pinkall,
Quaternionic holomorphic geometry: Plücker formula, Dirac eigenvalue estimates and energy estimates of harmonic 2-tori,
Invent. Math., 146 (2001), no. 3, 507-593.
-
F. Furuhata, L. Vrancken,
The Center Map of an Affine Immersion,
Results. Math. 49 (2006), 201-217.
-
P.B. Gilkey, S.Z. Nikcevic,
Geometrical Representations of Equiaffine Curvature Operators,
Results Math. 52 (2008), 281-287.
-
P.B. Gilkey, S.Z. Nikcevic, U. Simon,
Geometric Theory of Affine Curvature Tensors,
Results Math 56 (2009), 275-317.
-
P.B. Gilkey, S.Z. Nikcevic, U. Simon,
Geometric Realizations, Curvature Decompositions,
and Weyl Manifolds,
preprint, arXiv:1002.5027.
-
Z. Guo, L. Lin,
Generalized Rotation Submanifolds in a Space Form,
Results Math. 52 (2008), 289-298.
-
F.-F. Henrich, U. Pinkall,
The Space of Closed Curves in a Conformal 3-Manifold,
Oberwolfach Reports 24/2007.
-
F. Hirzebruch, U. Simon,
Nachruf auf Shiing-shen Chern.
Jahresbericht der Deutschen Mathematiker Vereinigung, 108 (2006), Heft 8, 197-217,
(Chinese translation: Mathematical Advance in Translation 3 (2008), 257-269).
-
Z. Hu, H. Li, U. Simon,
Schouten Curvature Functions on Locally Conformally Flat Riemannian Manifolds,
J. Geom. 88 (2008), 75-100.
-
Z. Hu, H. Li, U. Simon, L. Vrancken,
On Locally Strongly Convex Affine Hypersurfaces with Parallel Cubic Form, Part I,
Diff. Geom. Applications, vol. 27 (2009), 188-205.
-
Z. Hu, H. Li, L. Vrancken,
On Locally Strongly Convex Affine Hypersurfaces with Parallel Cubic Form, Part II,
J. Diff. Geom., submitted.
-
Z. Hu, H. Li, L. Vrancken,
A Characterization of the Calabi Product of Hyperbolic Affine Spheres,
Results Math. 52 (2008), 299-314.
-
Z. Hu, S. Nishikawa, U. Simon,
Critical Metrics of the Schouten Functional,
submitted.
-
Z. Hu, M. Scherfner, S. Zhai,
On Spacelike Hypersurfaces with Constant Scalar Curvature in the de Sitter Space,
Diff. Geom. Applications, vol. 25 (2007), 594-611.
-
Z. Hu, F. Yang,
A New Variational Characterization of Four Dimensional Manifolds with Constant Scalar Curvature,
Results in Math. 52 (2008), 315-322.
-
G. Kamberov, P. Norman, F. Pedit, U. Pinkall,
Quaternions, Spinors and Surfaces,
Contemporary Mathematics (299), American Mathematical Society (2002), Providence, RI.
-
M. Kossowski, M. Scherfner,
Total Curvature for C∞ -singular Surfaces with Limiting Tangent Bundle,
Annals of Global Analysis and Geometry 28, no. 2, (2005), 179-199.
-
K. Leschke, F. Pedit, U. Pinkall,
Willmore Tori in the 4-Sphere with Nontrivial Normal Bundle,
Math. Annalen , Vol. 332 (2005), 381-394
-
C. Lange, K. Polthier, U. Simon,
Zur Geometrie von Frühstückseiern,
Mathematische Semesterberichte 56 (2009), 1-14.
-
A. M. Li, H. Li, U. Simon,
Centroaffine Bernstein Problems,
Differential Geom. Appl., 20 (2004), no. 3, 331-356.
-
A. M. Li, F. Jia,
A Bernstein Property of Affine Maximal Hypersurfaces,
Ann. Global Analysis Geom., 23:359-372, 2003.
-
A. M. Li, F. Jia,
Locally Strongly Convex Hypersurfaces with Constant Affine Mean Curvature,
Differential Geom. Appl., 22 (2005), 199-214.
-
A. M. Li, F. Jia,
A Bernstein Property of Some Fourth Order Partial Differential Equations,
Results Math 56 (2009), 109-139.
-
A. M. Li, R. Xu,
A Cubic Form Differential Inequality with Applications to Affine Kähler-Ricci Flat Manifolds,
Results Math 54 (2009), 329-340.
-
A. M. Li, R. Xu,
A Rigidity Theorem for an Affine Kähler-Ricci Flat Graph,
Results Math 56 (2009), 141-164.
-
A. M. Li, R. Xu, U. Simon, F. Jia
Affine Bernstein Problems and Monge-Ampère Equations,
World Scientific (2010), Singapore;
ISBN 13 987-981-281-416-6
ISBN 10 981-281-416-7
-
H. Li, U. Simon,
Quantization of Curvature for Compact Surfaces in Sn,
Math. Z. 245 (2003), no. 2, 201-216.
-
H. Li, X. Wang,
Isotropic Lagrangian Submanifolds in Complex Euclidean Space and Complex Hyperbolic Space
Results Math 56 (2009), 387-403.
-
S. Li, G. Chen,
The Bernstein Property of Some Affine Kähler Scalar Flat Graph
Results Math 56 (2009), 165-175.
-
H. Liu,
Characterizations of Ruled Surfaces with Lightlike Ruling in Minkowski 3-Space,
Results Math 56 (2009), 357-368.
-
H. Liu, G. Liu,
Weingarten rotation surfaces in 3-dimensional de Sitter space,
Journal of Geometry 79 (2004).
-
Y. Lu, C. Scharlach,
Affine Hypersurfaces Admitting a Pointwise Symmetry,
Results Math. 48 (2005), 275-300.
-
T. Lusala, M. Scherfner, L. A. M. Souza Jr.,
Closed Willmore Hypersurfaces of S5(1) with Constant Mean and Scalar Curvature,
Asian J. Math. Vol. 9 No. 1 (2005), 65-78.
-
H. Ma, M. Schmies,
Examples of Hamiltonian Stationary Lagrangian Tori in CP2,
Geom. Dedicata 118 (2006), 173-183.
-
X. Ma,
Isothermic and S-Willmore Surfaces as Solutions to a Problem of Blaschke,
Results Math. 48 (2005), 301-309.
-
X. Ma,
Willmore Surfaces in Sn: Transforms and Vanishing Theorems,
PhD Thesis, TU Berlin (2005).
-
X. Ma, C. Wang,
Willmore Surfaces of Constant Möbius Curvature,
Ann. Global Anal. Geom. 32 (2007), 297-310.
-
X. Ma,
Adjoint Transform of Willmore Surfaces in Sn,
Manuscripta Math. 120 (2006), 163-179.
-
X. Ma, P. Wang,
Polar Transform of Spacelike Isothermic Surfaces in 4-Dimensional Lorentzian Space Forms,
Results Math. 52 (2008), 347-358
-
A. Martinez, F. Milan,
Some Results on Projectively Flat Affine Surfaces,
in: B. Opozda et al (eds.), PDEs, submanifolds and affine differential geometry. Proceedings conference and autumn school, Bedlewo, Poland, September 23-27, 2003. Warsaw: Polish Academy of Sciences, Institute of Mathematics.
Banach Center Publications 69 (2005), 163-169.
-
St. Müller, A. Schwenk-Schellschmidt, U. Simon,
Eigenvalue Equations in Curve Theory. Part II: Evolutes and Involutes,
Results in Math. 50 (2007), 109-124.
-
D. Nakajo,
A Representation Formula for Indefinite Improper Affine Spheres
Results Math 55 (2009), 139-159
-
V. Oliker,
On the Geometry of Convex Reflectors, II. Polar Reflectors,
Results Math. 52 (2008), 359-367
-
V. Oliker,
Kummer Configurations and Sm-Reflector Problems,
Results Math 56 (2009), 519-535.
-
V. Oliker, U. Simon,
Corrections: On the Geometry of Convex Reflectors,
PDEs, submanifolds and affine differential geometry, 269-270, Banach Center Publ. 69, Polish Acad. Sci., Warsaw, 2005.
-
B. Opozda,
Parallel Submanifolds,
Results Math 56 (2009), 231-244.
-
G. P. Peters,
Darboux Transformations: From Elastic Curves to Elastic Surfaces and Beyond,
in F. Dillen, I. van der Woestyne (eds.), Pure and Applied Differential Geometry - PADGE 2007 (2007), 203-212.
-
U. Pinkall,
Designing Cylinders with Constant Negative Curvature,
In Discrete Differential Geometry, Springer (2008), 57-66.
-
U. Pinkall, B. Springborn, S. Weißmann,
A New Doubly Discrete Analogue of Smoke Ring Flow and the Real Time Simulation of Fluid Flow,
J. Phys. A: Math. Theor. 40 (2007) 12563-12576.
-
L. Ramifidisoa,
Classification Results for Affine Surfaces and Centroaffine Tchebychev Hypersurfaces,
thesis, U. Valenciennes/F. (2008).
-
C. Rodriguez Montealegre, L. Vrancken,
Warped Product Minimal Lagrangian Immersion in Complex Projective Space,
Results Math 56 (2009), 405-420.
-
C. Scharlach,
Affine Geometry of Surfaces and Hypersurfaces in R4,
habilitation thesis, Fac. II, TU Berlin, 2006.
-
C. Scharlach,
Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 1,
Contributions to Algebra and Geometry 48(2) (2007), 469-491, arXiv:math/0510531v1 [math.DG].
-
C. Scharlach,
Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2,
SIGMA 5 (2009), 097, 22 pages, arXiv:0910.3609v1 [math.DG].
-
C. Scharlach, L. Vrancken,
Parallel Surfaces in Affine 4-Space,
Abh. Math. Sem. Univ. Hamburg 73 (2003), 167-179.
-
L. Sheng, G. Chen,
A Bernstein Property of Some Affine Kähler Scalar Flat Graph,
Results Math 56 (2009), 165-175.
-
M. Scherfner,
The Chern Conjecture for Isoparametric Hypersurfaces in Spheres: History and New Results,
in Proc. of the Symposium on the Differential Geometry of Submanifolds, Valenciennes (2007).
-
M. Scherfner, L. A. M. Sousa Jr., S. Weiss,
Closed Willmore Hypersurfaces of S5 with Constant Mean and Scalar Curvature,
preprint (2009).
-
M. Scherfner,L. Vrancken, S. Weiss,
On Isoparametric Hypersurfaces in S7,
submitted (2009).
-
M. Scherfner, S. Weiss,
Towards a Proof of the Chern Conjecture for Isoparametric Hypersurfaces in Spheres,
Proc. 33. South German Diff. Geom. Colloq. (2008).
-
M. Scherfner, S. Weiss, S.-T. Yau,
A Review of the Chern Conjecture for Isoparametric Hypersurfaces,
submitted (2009).
-
A. Schwenk-Schellschmidt,
Pedal Curves, Part I: Homogeneous Differential Equation,
Results. Math. 52 (2008), 369-382.
-
A. Schwenk-Schellschmidt, U. Simon,
Eigenwertgleichungen in der Kurventheorie - Charakterisierungen von Kurven, deren Abwicklung und Evolute durch Streckung ineinander überführbar sind,
Forschungsbericht TFH Berlin (2006), 20-23,
ISBN 3-93576-07-3
Hrsg. R. Thuemer, G. Goerlitz.
-
A. Schwenk-Schellschmidt, U. Simon,
Codazzi-Equivalent Affine Connections
Results Math 56 (2009), 211-229.
-
A. Schwenk-Schellschmidt, U. Simon, L. Vrancken,
Codazzi-Equivalent Riemannian Metrics,
Asian Math. J., in print.
-
U. Simon,
The Centroaffine Volume of Generalized Geodesic Balls under Inversion at the Sphere,
Results Math. 43 (2003), no. 3-4, 343-358.
-
U. Simon,
Affine Hypersurface Theory Revisited: Gauge Invariant Structures (English version),
Russian Mathematics (Izv. vuz) 48 (2004), 48-73.
-
U. Simon,
Affine Hypersurface Theory Revisited: Gauge Invariant Structures,
Russian Mathematics (Izv. vuz) 11 (2005), 53-81 (in Russian).
-
U. Simon,
Yau's Problem on a Characterization of Rotational Ellipsoids,
Asian Math. J. 11 (2007), 361-372.
-
U. Simon,
Schouten Curvature Functionals on Conformally Flat Manifolds,
Proc. conf. Riemannian Geometry and Applications Brasov, June 21-25, 2007, Trans. U. Brasov, Vol 14(49) Series B (2007), Supplement pp. 293-324, ISSN 1223-964X.
-
U. Simon,
A Survey on Codazzi Tensors,
Forum Berliner Math. Gesellschaft 8 (2009), 97-106
-
U. Simon, H. Trabelsi, L. Vrancken,
Complete Hyperbolic Tchebychev Hypersurfaces,
J. Geom., vol. 89 (2008), 148-159.
-
U. Simon, R. Xu,
Geometric Modelling Techniques for the Solution of certain Monge-Ampère Equations,
submitted.
-
B. Springborn, P. Schröder, U. Pinkall,
Conformal Equivalence of Triangle Meshes,
to appear in ACM Transactions on Graphics (SIGGRAPH 2008).
-
H. Trabelsi,
Propriete de l'application centre d'une hypersurface affine,
Thesis U Valenciennes/F, 2006.
-
B. Wang, A. M. Li,
Euclidean Complete Affine Hypersurfaces with Negative Constant Affine Mean Curvature,
Results in Math. 52 (2008), 383-398.
-
C. P. Wang,
Weierstrass Representations of Laguerre Minimal Surfaces in R3,
Results Math. 52 (2008), 399-408
-
C. P. Wang, Z. Hu, H. Li,
Classification of Möbius Isoparametric Hypersurfaces in S^5,
Monatshefte für Mathematik 151 (2007), 201-222.
-
C. P. Wang, X. Ma,
Willmore Surface of Constant Möbius Curvature,
Annals of Global Analysis and Geometry 32 (2007), 297-310.
-
C. P. Wang, C. Nie, X. Ma,
Conformal CMC-surfaces in Lorentzian Space Forms,
Chinese Annals of Mathematics 28 (2007), Ser.B, 299-310.
-
S. Weißmann, U. Pinkall,
Real-Time Interactive Simulation of Smoke using Discrete Integrable Vortex Filaments,
Workshop in Virtual Reality Interactions and Physical Simulation "VRIPHYS" (2009), 1-10 , (online).
-
M. Wiehe,
Regular Intersections of Quadrics and Parallel Submanifolds,
Manuscr. Math. 111 (2003), 529-547.
-
R. Xu,
Bernstein Properties for Some Relative Parabolic Affine Hyperspheres,
Results Math. 52 (2008), 409-422.
-
Y. Yang, H.L. Liu,
Minimal Centroaffine Immersions of Codimension Two,
Results Math. 52 (2008), 423-437.
-
Y. Yang, Y. Yu, H. Liu,
Centroaffine Translation Surfaces in R3,
Results Math 56 (2009), 197-210.
Editorial Work
-
B. Opozda, U. Simon, M. Wiehe, PDEs, Submanifolds and Affine
Differential Geometry, Proc. Conference Banach Center Bedlewo 2003, Banach Center Publications 69 (2005).
-
U. Simon, Co-editor of Results in Mathematics since 1994, Editorial board since 2000, Assoc. Manag. Ed. 2007
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U. Simon, Co-Editor: International Electronic Journal of Geometry, www.iejgeo.com
-
U. Simon, H. Wefelscheid, L. Vrancken,
Results Math. 56 (2009),
Volume in memory of K. Nomizu.
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