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

Boris Springborn

TU Berlin, MA 8-3
Strasse des 17. Juni 136
10623 Berlin
office MA 871
tel +49 30 314 23617
fax +49 30 314 79282
secretary (MA 8-3)
Mathias Kall
tel +49 30 314 29273


Projects A01, A11 in SFB/Transregio 109 "Discretization in Geometry and Dynamics"

Office hours / Sprechstunde

vorlesungsfreie Zeit nach Vereinbarung


Summer 2017 Differentialgeometrie I
Komplexe Analysis I
Winter 2016/17 Forschungsfreisemester
previous semesters

Mündliche Modulprüfungen (oral exams)

Nächste Termine:

Bitte vereinbaren Sie Ihren Prüfungstermin mit Herrn Kall, Raum MA 873.

Please make arrangements with my secratary Mathias Kall, room MA 873.



M. Joswig, R. Löwe, and B. Springborn. Secondary fans and secondary polyhedra of punctured Riemann surfaces. arXiv:1708.08714 [math.MG], 2017.

B. Springborn. Hyperbolic polyhedra and discrete uniformization. arXiv:1707.06848 [math.MG], 2017.

B. Springborn. The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms. arXiv:1702.05061 [math.GT], 2017.

Journal articles

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.2000.7.3.5.

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.

Some Old Stuff

Doyle Spiral Demo (A Java-webstart application. For info on Doyle spirals see this article.)
Gallery of Polyhedral Types (Needs Java-plugin.)
Some pictures of discrete minimal surfaces (See also Stefan Sechelmann's homepage.)
Boris Springborn
Last modified: Friday, 01-Sep-2017 16:50:46 CEST .