A discrete Schwarz minimal surface      

DFG Research Unit
Polyhedral Surfaces

      TU Berlin
   

Home

Projects

Publications

People

Seminar

Events

Software

TU Geometry

Matheon

     

Publications

  • Minkowski decomposition of associahedra and the computation of Möbius inversion , 2012
    Preprint at arXiv
    (Carsten Lange)

  • Non projectability of polytope skeleta , 2012
    Advances in Mathematics, Vol. 229 (1), 79-101
    (Thilo Rörig, Raman Sanyal)

  • Discretization of asymptotic line parametrizations using hyperboloid surface patches , 2011
    Accepted at Geometriae Dedicata
    (Emanuel Huhnen-Venedey, Thilo Rörig)

  • Optimal Topological Simplification of Discrete Functions on Surfaces , 2011
    Discrete and Computational Geometry, 2012, Volume 47, Number 2, Pages 347-377
    (Ulrich Bauer, Carsten Lange, Max Wardetzky)

  • Permutahedra and generalized associahedra , 2011
    Advances in Mathematics 226 (2011), no. 1, 608-640.
    (Christophe Hohlweg, Carsten Lange, Hugh Thomas)

  • Combinatorics of Minkowski decomposition of associahedra , 2011
    CCCG 2011
    (Carsten Lange)

  • Minkowski decompositions of associahedra , 2011
    FPSAC 2011
    (Carsten Lange)

  • Curvature line parametrized surfaces and orthogonal coordinate systems. Discretization with Dupin cyclides, 2011
    Geometriae Dedicata (online first), Preprint at arXiv:1101.5955 [math.DG]
    (A.I. Bobenko, E. Huhnen-Venedey)

  • Classification of integrable discrete equations of octahedron type, 2010
    Internat. Math. Research Notices 2011, doi:10.1093/imrn/rnr083, 1-68,
    [pdf file], [html file], Preprint (2010) arXiv:1011.3527 [nlin.SI]
    (V.E. Adler, A.I. Bobenko, Yu.B. Suris)

  • Computational Approach to Riemann Surfaces, 2011
    Lecture Notes in Mathematics, Vol. 2013, Springer, 257 p.
    (A.I. Bobenko, Ch. Klein, eds.)

  • Introduction to Compact Riemann Surfaces
    In: Computational Approach to Riemann Surfaces, A.I. Bobenko, Ch. Klein (Eds.), Lecture Notes in Mathematics, Vol. 2013, Springer, 2011, 3-64
    (A.I. Bobenko)

  • Conformal Structures and Period Matrices of Polyhedral Surfaces
    In: Computational Approach to Riemann Surfaces, A.I. Bobenko, Ch. Klein (Eds.), Lecture Notes in Mathematics, Vol. 2013, Springer, 2011, 213-226
    [pdf file], Preprint (2009) arXiv:0909.1305 [math.DG]
    (A.I. Bobenko, Ch. Mercat, M. Schmies)

  • Finite motions from periodic frameworks with added symmetry , October 2010
    International Journal of Solids and Structures, to appear
    (Elissa Ross, Bernd Schulze, Walter Whiteley)

  • On the area discrepancy of triangulations of squares and trapezoids , October 2010
    submitted
    (Bernd Schulze)

  • Polyhedral surfaces in wedge products , July 2010
    Geom. Dedicata, Vol. 151 (1), 155-173
    (Thilo Rörig, Günter M. Ziegler)

  • Three non-equivalent realizations of the associahedron, June 2010
    Preprint (arXiv:1006.3487)
    (Cesar Ceballos, Günter M. Ziegler)

  • The orbit rigidity matrix of a symmetric framework , June 2010
    Discrete & Comput. Geom., to appear
    (Bernd Schulze, Walter Whiteley)

  • Symmetric Laman theorems for the groups C_2 and C_s , 2010
    The Electronic Journal of Combinatorics 17 (2010), No.1, R154, 1-61
    (Bernd Schulze)

  • Symmetry as a sufficient condition for a finite flex , 2010
    SIAM Journal on Discrete Mathematics 24 (2010), No. 4, 1291-1312
    (Bernd Schulze)

  • When is a symmetric body-bar structure isostatic? , 2010
    International Journal of Solids and Structures 47 (2010), 2745-2754
    (Simon Guest, Bernd Schulze, Walter Whiteley)

  • Symmetric versions of Laman's Theorem , 2010
    Discrete Comput. Geom. 44 (2010), No. 4, 946-972
    (Bernd Schulze)

  • Block-diagonalized rigidity matrices of symmetric frameworks and applications , 2010
    Contributions to Algebra and Geometry 51 (2010), No. 2, 427-466
    (Bernd Schulze)

  • Totally splittable polytopes, 2010
    Discrete Comput. Geom. 44 (2010), no. 1, 149-166, 52Bxx.
    (Sven Herrmann, Michael Joswig)

  • Tropical and ordinary convexity combined, 2010
    Adv. Geom. 10 (2010), no. 2, 333-352, 14T05 (52A01).
    (Michael Joswig, Katja Kulas)

  • Discrete conformal maps and ideal hyperbolic polyhedra, 2010
    (A.I. Bobenko, U. Pinkall, B. Springborn)

  • Uniform Convergence of Discrete Curvatures from Nets of Curvature Lines , May 2010
    Discrete and Computational Geometry 43:4 (2010), 798-823.
    (Ulrich Bauer, Konrad Polthier and Max Wardetzky)

  • Drawing polytopal graphs with polymake , February 2010
    Computing and Visualization in Science, Volume 13, Number 2
    (Ewgenij Gawrilow, Michael Joswig, Thilo Rörig, Nikolaus Witte)

  • Rigidity of quasicrystallic and Z^\gamma-circle patterns , January 2010
    (Ulrike Bücking)

  • Equivelar and d-covered triangulations of surfaces. II. Cyclic triangulations and tessellations, January 2010
    (Frank H. Lutz)

  • Equivelar and d-covered triangulations of surfaces. I, January 2010
    (Frank H. Lutz, Thom Sulanke, Anand K. Tiwari, and Ashish K. Upadhyay)

  • Tropical convex hull computations, 2009
    Tropical and idempotent mathematics, 193-212, Contemp. Math., 495, Amer. Math. Soc., Providence, RI, 2009, 52A30 (14T05 52C45).
    (Michael Joswig)

  • How to draw tropical planes, 2009
    Electron. J. Combin. 16 (2009), no. 2, Special volume in honor of Anders Bjorner, Research Paper 6, 26 pp.
    (Sven Herrmann, Anders Jensen, Michael Joswig, Bernd Sturmfels)

  • On the Lagrangian structure of integrable quad-equations, 2009
    Lett. Math. Phys. 92, No.1 (2010), 17-31
    (A.I. Bobenko, Yu.B. Suris)

  • The dunce hat and a minimal non-extendably collapsible 3-ball, December 2009
    Electronic Geometry Models (to appear)
    (Bruno Benedetti, Frank H. Lutz)

  • Examples of infinitesimally flexible 3--dimensional hyperbolic cone-manifolds, Oktober 2009
    J. Math. Soc. Japan. (to appear)
    (Ivan Izmestiev)

  • Gauss images of hyperbolic cusps with convex polyhedral boundary, August 2009
    Trans. Am. Math. Soc. (to appear)
    (F. Fillastre, I. Izmestiev)

  • On locally constructible spheres and balls, February 2009
    Acta Mathematica, to appear
    (Bruno Benedetti, Günter M. Ziegler)

  • A curvature theory for discrete surfaces based on mesh parallelity, January 2009
    Math. Annalen 348 (2010), 1-24.
    (A.I. Bobenko, H. Pottmann, J. Wallner)

  • Splitting polytopes, 2008
    Münster J. Math. 1 (2008), 109-141, 52B12.
    (Sven Herrmann, Michael Joswig)

  • Algorithmische Geometrie (German) [Algorithmic geometry], 2008
    Polyedrische und algebraische Methoden. [Polyhedral and algebraic methods] Vieweg Studium: Aufbaukurs Mathematik. [Vieweg Studies: Mathematics Course] Vieweg, Wiesbaden, 2008. vi+265 pp. ISBN: 978-3-8348-0281-1, 51-01 (13P10 52-01).
    (Michael Joswig, Thorsten Theobald)

  • Integrable discrete nets in Grassmannians, December 2008
    Lett. Math. Phys. 89 (2009) 131-139
    (V.E. Adler, A.I. Bobenko, Yu.B. Suris)

  • Discrete Differential Geometry: Integrable Structure, December 2008
    Graduate Studies in Mathematics, Vol. 98, AMS, xxiv + 404 p; hardcover.
    (A.I. Bobenko, Yu.B. Suris)

  • Zonotopes with Large 2D Cuts (eg-model) , October 2008
    (Thilo Rörig, Nikolaus Witte, Günter M. Ziegler)

  • Polyhedral Surfaces, Polytopes, and Projections, September 2008
    Dissertation, TU Berlin, 126 pages.
    (Thilo Rörig)

  • Approximation of conformal mappings by circle patterns, June 2008
    Geom. Dedicata, 137 (2008), 163-197.
    (Ulrike Bücking)

  • Zonotopes with Large 2D Cuts , May 2008
    Discrete & Computational Geometry (4) 42 (2009), 527-541
    (Thilo Rörig, Nikolaus Witte, Günter M. Ziegler)

  • f-Vectors of 3-Manifolds, May 2008
    Electron. J. Comb. 16, No. 2, Research Paper R13, 33 p. (2009).
    (Frank H. Lutz, Thom Sulanke, and Ed Swartz)

  • Projective background of the infinitesimal rigidity of frameworks, April 2008
    Geom. Dedicata 140, No.1 (2009), 183-203
    (I.Izmestiev)

  • Discrete holomorphic geometry I. Darboux transformations and spectral curves, March 2008
    Crelle's J. Reine Angew. Math. (to appear)
    (Christoph Bohle, Franz Pedit, Ulrich Pinkall)

  • Approximation of conformal mappings by circle patterns and discrete minimal surfaces., February 2008
    PhD thesis, Technische Universität Berlin, published online.
    (Ulrike Bücking)

  • Discrete Differential Geometry, January 2008
    Reihe Oberwolfach Seminars, Vol. 38, Birkhäuser Basel, vii + 341 p.
    (A.I. Bobenko, P. Schröder, J.M. Sullivan, G.M. Ziegler, eds.)

  • Affine buildings and tropical convexity, 2007 Albanian J. Math. 1 (2007), no. 4, 187-211.
    (Michael Joswig, Bernd Sturmfels, Josephine Yu)

  • Bounds on the f-vectors of tight spans, 2007
    Contrib. Discrete Math. 2 (2007), no. 2, 161-184 (electronic), 52B70 (05C90).
    (Sven Herrmann, Michael Joswig)

  • Products of foldable triangulations, 2007
    Adv. Math. 210 (2007), no. 2, 769-796.
    (Michael Joswig, Nikolaus Witte)

  • Minimal surfaces from circle patterns: Boundary value problems, examples, 2007
    "Discrete Differential Geometry", Reihe Oberwolfach Seminars, Vol. 38, Birkhäuser Basel, pages 37-56.
    A.I. Bobenko, P. Schröder, J.M. Sullivan, G.M. Ziegler (eds.)
    (Ulrike Bücking)

  • On the infinitesimal rigidity of polyhedra with vertices in convex position, November 2007
    Pacific J. Math. (to appear)
    (I. Izmestiev, J.-M. Schlenker)

  • Non-rational configurations, polytopes, and surfaces, October 2007
    Mathematical Intelligencer, (3) 30 (2008), 36-42.
    (Günter M. Ziegler)

  • Polyhedral tori with minimal coordinates, September 2007
    Electronic Geometry Models, No. 2008.10.001 (2008)
    (Stefan Hougardy, Frank H. Lutz, and Mariano Zelke)

  • Discrete Koenigs nets and discrete isothermic surfaces, September 2007
    Internat. Math. Research Notices (2009) 1976-2012
    (A.I. Bobenko, Yu.B. Suris)

  • Hyperbolic cusps with convex polyhedral boundary, August 2007
    Geom. Topol. 13:1 (2009), 457-492.
    (F. Fillastre, I. Izmestiev)

  • Surfaces from Circles, July 2007
    "Discrete Differential Geometry", Reihe Oberwolfach Seminars, Vol. 38, Birkhäuser Basel, pages 3-35.
    A.I. Bobenko, P. Schröder, J.M. Sullivan, G.M. Ziegler (eds.)
    (A.I. Bobenko)

  • An Algorithm for the Construction of Intrinsic Delaunay Triangulations with Applications to Digital Geometry Processing, 2007
    Computing 81:2-3 (2007), 199-213
    (M. Fischer, B. Springborn, P. Schröder, A.I. Bobenko)

  • Knotted polyhedral tori, July 2007
    (Frank H. Lutz and Nikolaus Witte)

  • Curvature line parametrization from circle patterns, June 2007
    (A.I. Bobenko, S.P. Tsarev)

  • A small polyhedral Z-acyclic 2-complex in R4, May 2007
    Electronic Geometry Models, No. 2008.11.001 (2008)
    (Frank H. Lutz and Günter M. Ziegler)

  • Discrete nonlinear hyperbolic equations. Classification of integrable cases, May 2007
    Functional Anal. and Appl. 43, No.1 (2009)
    (V.E. Adler, A.I. Bobenko, Y.B. Suris)

  • Colin de Verdière number and graphs of polytopes, April 2007
    accepted at Israel J. Math.
    (I. Izmestiev)

  • A variational proof of Alexandrov's convex cap theorem, March 2007
    Discrete Comput. Geom. 40:4 (2008), 561-585.
    (I. Izmestiev)

  • Geometry of multi-layer freeform structures for architecture, 2007
    ACM Trans. Graphics 26(3) (2007), SIGGRAPH 2007
    (H. Pottmann, Y. Liu, J. Wallner, A. Bobenko, W. Wang)

  • Flexible object hierarchies in polymake (extended abstract), 2006
    Mathematical software ICMS 2006, 219-221, Lecture Notes in Comput. Sci., 4151, Springer, Berlin, 2006, 52-04 (52B55).
    (Ewgenij Gawrilow, Michael Joswig)

  • Computing optimal Morse matchings, 2006
    SIAM J. Discrete Math. 20 (2006), no. 1, 11-25 (electronic).
    (Michael Joswig, Marc E. Pfetsch)

  • Isothermic surfaces in sphere geometries as Moutard nets, October 2006
    Proc. Royal. Soc. A. 463 (2007) 3171-3193
    (A.I. Bobenko, Y.B. Suris)

  • Isomorphism free lexicographic enumeration of triangulated surfaces and 3-manifolds, October 2006
    Eur. J. Comb. (2009), doi:10.1016/j.ejc.2008.12.016
    (Thom Sulanke and Frank H. Lutz)

  • Alexandrov's theorem, weighted Delaunay triangulations, and mixed volumes, September 2006
    Ann. Inst. Fourier, 58:2 (2008), 447-505.
    (A.I. Bobenko, I. Izmestiev)

  • On organizing principles of Discrete Differential Geometry. Geometry of spheres, August 2006
    Russian Math. Surveys, 62:1 (2007)
    (A.I. Bobenko, Y.B. Suris)

  • Surface realization with the intersection edge functional, August 2006
    Exp. Math. 19 (2010), 79-92.
    (Stefan Hougardy, Frank H. Lutz, and Mariano Zelke)

  • Combinatorial 3-manifolds with 10 vertices, April 2006
    Beitr. Algebra Geom. 49, 97-106 (2008)
    (Frank H. Lutz)

  • Polyhedra of genus 3 with 10 vertices and minimal coordinates, April 2006
    Electronic Geometry Models, No. 2006.02.001 (2007)
    (Stefan Hougardy, Frank H. Lutz, and Mariano Zelke)

  • Polytope propagation on graphs, 2005
    Algebraic statistics for computational biology, 181-192, Cambridge Univ. Press, New York, 2005, 60J20 (05C20 60J10 92D15).
    (Michael Joswig)

  • Complexes of discrete Morse functions, 2005
    Discrete Math. 302 (2005), no. 1-3, 39-51.
    (Manoj K. Chari, Michael Joswig)

  • Tropical halfspaces, 2005
    Combinatorial and computational geometry, 409-431, Math. Sci. Res. Inst. Publ., 52, Cambridge Univ. Press, Cambridge, 2005.
    (Michael Joswig)

  • One-point suspensions and wreath products of polytopes and spheres, 2005
    J. Combin. Theory Ser. A 110 (2005), no. 2, 193-216.
    (Michael Joswig, Frank H. Lutz)

  • Balanced Triangulations of Lattice Polytopes, August 2005
    (M. Joswig, N. Witte)

  • Geometric Reasoning with polymake, July 2005
    (E. Gawrilow, M. Joswig)

  • Polyhedra of genus 2 with 10 vertices and minimal coordinates, July 2005
    Electronic Geometry Models, No. 2005.08.001 (2007)
    (Stefan Hougardy, Frank H. Lutz, and Mariano Zelke)

  • Enumeration and random realization of triangulated surfaces, June 2005
    "Discrete Differential Geometry", Reihe Oberwolfach Seminars, Vol. 38, Birkhäuser Basel, pages 235-253.
    A.I. Bobenko, P. Schröder, J.M. Sullivan, G.M. Ziegler (eds.)
    (Frank H. Lutz)

  • Discrete Willmore Flow, June 2005
    Eurographics Symposium on Geometry Processing (2005), M.Desbrun, H.Pottmann (eds.)
    (A.I. Bobenko, P. Schröder)

  • Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I, June 2005
    (Ekkehard G. Köhler and Frank H. Lutz)

  • Triangulated Manifolds with Few Vertices: Combinatorial Manifolds, June 2005
    (Frank H. Lutz)

  • Discrete differential geometry. Consistency as integrability, May 2005
    A preliminary version of a book, 157pp.
    (A.I. Bobenko, Y.B. Suris)

  • A discrete Laplace-Beltrami operator for simplicial surfaces, March 2005
    Discrete and Computational Geometry 38:4 (2007) 740-756
    (A.I. Bobenko, B. Springborn)

  • Neighborly cubical polytopes and spheres, March 2005
    (M. Joswig, T. Rörig)

  • Computing optimal discrete Morse functions, 2004
    Workshop on Graphs and Combinatorial Optimization, 191-195 (electronic), Electron. Notes Discrete Math., 17, Elsevier, Amsterdam, 2004, 90C57.
    (Michael Joswig, Marc E. Pfetsch)

  • Convex hulls, oracles, and homology, 2004
    J. Symbolic Comput. 38 (2004), no. 4, 1247-1259.
    (Michael Joswig, Günter M. Ziegler)

  • Convex polytopes: Extremal constructions and f-vector shapes, 2004
    "Geometric Combinatorics", Park City Mathematical Institute (PCMI), American Math. Society, Providence, RI, 2007, pages 617-691.
    E. Miller, V. Reiner, and B. Sturmfels (eds.)
    (Günter M. Ziegler; with an appendix by Th. Schröder and N. Witte)

  • Polyhedral surfaces of high genus, December 2004
    "Discrete Differential Geometry", Reihe Oberwolfach Seminars, Vol. 38, Birkhäuser Basel, pages 191-213.
    A.I. Bobenko, P. Schröder, J.M. Sullivan, G.M. Ziegler (eds.)
    (G.M. Ziegler)
    • on top
    Emanuel Huhnen-Venedey . 11.01.2013.