Fakultät II - Mathematik und Naturwissenschaften Institut für Mathematik AG Geometrie und Mathematische Physik

Boris Springborn

Professor

Projects

A01 Discrete Riemann surfaces in SFB/Transregio 109 Discretization in Geometry and Dynamics

Teaching

Sprechstunde / office hours

Mündliche Prüfungen (oral exams)

Pr�fungstermine w�hrend der Vorlesungszeit im Wintersemester 25/26 werden noch bekanntgegeben.

Bitte vereinbaren Sie Ihren Prüfungstermin mit Frau Gabler.
Please make arrangements with Ms. Gabler.

Editorial activities

Publications

Book

G. Fischer and B. Springborn. Lineare Algebra. Eine Einf�hrung f�r Studienanf�nger. Grundkurs Mathematik. Springer, 20th edition, 2025. doi.org/10.1007/978-3-662-71261-0.

Journal articles

Boris Springborn. The worst approximable rational numbers. J. Number Theory, 263:153--205, 2024. doi:10.1016/j.jnt.2024.04.013.

M. Gillespie, B. Springborn, and K. Crane. Discrete conformal equivalence of polyhedral surfaces. ACM Trans. Graph., 40(4), 2021. doi:10.1145/3450626.3459763.

U. Pinkall and B. Springborn. A discrete version of Liouville's theorem on conformal maps. Geom. Dedicata, 214:389--398, 2021. doi:10.1007/s10711-021-00621-2.

B. Springborn. Ideal hyperbolic polyhedra and discrete uniformization. Discrete Comput. Geom., 64(1):63--108, 2020. doi:10.1007/s00454-019-00132-8.

M. Joswig, R. Löwe, and B. Springborn. Secondary fans and secondary polyhedra of punctured Riemann surfaces. Exp. Math., 29(4):426--442, 2020. Published online 04 Jun 2019. doi:10.1080/10586458.2018.1477078.

B. Springborn. The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms. Enseign. Math., 63(3-4):333--373, 2017. doi:10.4171/LEM/63-3/4-5.

S. Born, U. Bücking, and B. Springborn. Quasiconformal dilatation of projective transformations and discrete conformal maps. Discrete Comput. Geom., 57(2):305--317, 2017. doi:10.1007/s00454-016-9854-7.

R. Richter, J. E. Kyprianidis, B. Springborn, and M. Alexa. Constrained modelling of 3-valent meshes using a hyperbolic deformation metric. Computer Graphics Forum, 36(6):62--75, 2017. doi:10.1111/cgf.12805.

A. I. Bobenko, U. Pinkall, and B. Springborn. Discrete conformal maps and ideal hyperbolic polyhedra. Geom. Topol., 19(4):2155--2215, 2015. doi:10.2140/gt.2015.19.2155.

I. Izmestiev, R. B. Kusner, G. Rote, B. Springborn, and J. M. Sullivan. There is no triangulation of the torus with vertex degrees 5,6,...,6,7 and related results: geometric proofs for combinatorial theorems. Geom. Dedicata, 166:15--29, 2013. doi:10.1007/s10711-012-9782-5.

B. Springborn, P. Schröder, and U. Pinkall. Conformal equivalence of triangle meshes. ACM Trans. Graph., 27(3):77:1--77:11, August 2008. Proceedings of ACM SIGGRAPH. doi:10.1145/1360612.1360676.

B. Springborn. A variational principle for weighted Delaunay triangulations and hyperideal polyhedra. J. Differential Geom., 78(2):333--367, 2008. doi:10.4310/jdg/1203000270.

U. Pinkall, B. Springborn, and S. Weißmann. A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow. J. Phys. A, 40(42):12563--12576, 2007. doi:10.1088/1751-8113/40/42/S04.

A. I. Bobenko and B. Springborn. A discrete Laplace-Beltrami operator for simplicial surfaces. Discrete Comput. Geom., 38(4):740--756, 2007. doi:10.1007/s00454-007-9006-1.

M. Fisher, B. Springborn, P. Schröder, and A. I. Bobenko. An algorithm for the construction of intrinsic Delaunay triangulations with applications to digital geometry processing. Computing, 81(2-3):199--213, 2007. doi:10.1007/s00607-007-0249-8.

A. I. Bobenko, T. Hoffmann, and B. Springborn. Minimal surfaces from circle patterns: geometry from combinatorics. Ann. of Math. (2), 164(1):231--264, 2006. doi:10.4007/annals.2006.164.231.

L. Kharevych, B. Springborn, and P. Schröder. Discrete conformal mappings via circle patterns. ACM Trans. Graph., 25(2):412--438, April 2006. doi:10.1145/1138450.1138461.

B. Springborn. A unique representation of polyhedral types. Centering via Möbius transformations. Math. Z., 249(3):513--517, 2005. doi:10.1007/s00209-004-0713-5.

A. I. Bobenko and B. Springborn. Variational principles for circle patterns and Koebe's theorem. Trans. Amer. Math. Soc., 356(2):659--689, 2004. doi:10.1090/S0002-9947-03-03239-2.

A. I. Bobenko, T. V. Pavlyukevich, and B. Springborn. Hyperbolic constant mean curvature one surfaces: spinor representation and trinoids in hypergeometric functions. Math. Z., 245(1):63--91, 2003. doi:10.1007/s00209-003-0511-5.

B. Springborn. The toy top, an integrable system of rigid body dynamics. J. Nonlinear Math. Phys., 7(3):386--410, 2000. doi:10.2991/jnmp.2000.7.3.6.

Book chapters

H. Kouřimská, L. Skuppin, and B. Springborn. A variational principle for cyclic polygons with prescribed edge lengths. In A. I. Bobenko, editor, Advances in discrete differential geometry, pages 177--195. Springer, Berlin, 2016. doi:10.1007/978-3-662-50447-5_5.

A. I. Bobenko, S. Sechelmann, and B. Springborn. Discrete conformal maps: boundary value problems, circle domains, Fuchsian and Schottky uniformization. In A. I. Bobenko, editor, Advances in discrete differential geometry, pages 1--56. Springer, Berlin, 201. doi:10.1007/978-3-662-50447-5_1.

Conference proceedings

B. Springborn. Constructing circle patterns using a new functional. In Visualization and mathematics III, Math. Vis., pages 59--68. Springer, Berlin, 2003. doi:10.1007/978-3-662-05105-4_3.

B. Springborn. Bonnet pairs in the 3-sphere. In Differential geometry and integrable systems (Tokyo, 2000), volume 308 of Contemp. Math., pages 297--303. Amer. Math. Soc., Providence, RI, 2002. doi:10.1090/conm/308/05326.

PhD thesis

B. Springborn. Variational principles for circle patterns. PhD thesis, Technische Universität Berlin, 2003. Advisor: A. I. Bobenko. doi:10.14279/depositonce-767.

Other publications

A. I. Bobenko and B. Springborn. Diskretisierung in Geometrie und Dynamik---elastische Stäbe und Rauchringe. Mitt. Dtsch. Math.-Ver., 21(4):218--224, 2013. doi:10.1515/dmvm-2013-0085.

B. Springborn. Stein--Schere--Papier. In K. Biermann, M. Grötschel, and B. Lutz-Westphal, editors, Besser als Mathe: Moderne angewandte Mathematik aus dem Matheon zum Mitmachen, pages 23--26. Vieweg Teubner, Wiesbaden, 2010. doi:10.1007/978-3-8348-9380-2_4.

Old Stuff

• circlepatternsoftware as described in my phd thesis. (The link in the thesis does not work anymore.)
• Some pictures of discrete minimal surfaces (See also Stefan Sechelmann's homepage.)