TU Berlin Fakultät II
Institut für Mathematik
     

DFG-Project Geometric Problems and Special PDEs 2003-2010

       

  

Geometry Group

Members

Projects

Lehre

Seminare

Images, Videos, and Games

Virtual Math Labs

Software

Contact



      

People at TU Berlin

Prof. Dr. U. Pinkall (head)
Prof. Dr. U. Simon (head)
Prof. Dr. M. Scherfner
Prof. Dr. A. Schwenk (BHT Berlin, assoc. member)
Priv.-Doz. Dr. C. Scharlach
Dr. C. Bohle
Dr. G. P. Peters
S. Weißmann
F. J. Knöppel
 
A. Gillmeister (secretary), Tel.: 314 29281, Fax: 314 29260
 
Technische Universität Berlin
Fakultät II: Mathematik und Naturwissenschaften
Institute of Mathematics, MA 8-3
Straße des 17. Juni 136
10623 Berlin
Germany


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

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



 

Guests 2010

NameOriginPeriod
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
 

Guests 2009

NameOriginPeriod
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
 

Guests 2008

NameOriginPeriod
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
 

Guests 2007

NameOriginPeriod
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
 

Guests 2006

NameOriginPeriod
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
 

Guests 2005

NameOriginPeriod
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
 

Guests 2004

NameOriginPeriod
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
 

Guests 1997-2003

See the old homepage.


Seminars


Doctoral Thesis / Habilitation Thesis

  • 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).
  • 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).
  • 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).
  • 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

  • N. Abe, K. Hasegawa,
    A Generalization of Cartan's Identities for Isoparametric Hypersurfaces and Its Applications,
    Results Math. 52 (2008), 197-210.
  • J. A. Aledo, A. Martínez and F. Milán,
    Affine Maximal Surfaces with Singularities,
    Results Math. 56 (2009), 91-107.
  • T. Binder,
    Relative Tchebychev hypersurfaces which are also translation hypersurfaces,
    Hokkaido Math. J 38 (2009), 97-110.
  • 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.
  • N. Blazic, P. Gilkey, S. Nikčević, U. Simon,
    The Spectral Geometry of the Weyl Conformal Tensor,
    Banach Center Publications 69 (2005), 195-203.
  • N. Blazic, P. Gilkey, S. Nikčević, and U. Simon,
    Algebraic Theory of Affine Curvature Tensors,
    Archivum mathematicum (Brno) 42 (2006), supplement, 147-168.
  • 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].
  • 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].
  • 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].
  • 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.
  • S. Born, M.Kossowski, M. Scherfner,
    Characteristic Classes for Pseudo Riemannian Minifolds with Volume-Resolvable Metric Singularities,
    preprint (2009).
  • M. Brozos-Vázquez, P. Gilkey, S. Nikčević, U. Simon,
    Projectively Osserman Manifolds,
    Publications Mathematicae (Debrecen) 72 (2008), 359-370.
  • M. Brozos-Vázquez, P. Gilkey, S. Nikčević, R. Vázquez-Lorenzo,
    Geometric Realizations of Para-Hermitian Curvature Models,
    Results Math 56 (2009), 319-333.
  • 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.
  • 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
  • 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
  • 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.

Felix J. Knöppel . 12.10.2011.