Volume 25, issue 2 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Quadratic differentials and circle patterns on complex projective tori

Wai Yeung Lam

Geometry & Topology 25 (2021) 961–997
Bibliography
1 S I Agafonov, A I Bobenko, Discrete Zγ and Painlevé equations, Int. Math. Res. Not. 2000 (2000) 165 MR1747617
2 O Baues, The deformation of flat affine structures on the two-torus, from: "Handbook of Teichmüller theory, IV" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 19, Eur. Math. Soc. (2014) 461 MR3289710
3 A F Beardon, T Dubejko, K Stephenson, Spiral hexagonal circle packings in the plane, Geom. Dedicata 49 (1994) 39 MR1261573
4 A I Bobenko, U Pinkall, B A Springborn, Discrete conformal maps and ideal hyperbolic polyhedra, Geom. Topol. 19 (2015) 2155 MR3375525
5 A Bobenko, M Skopenkov, Discrete Riemann surfaces : linear discretization and its convergence, J. Reine Angew. Math. 720 (2016) 217 MR3565974
6 A I Bobenko, B A Springborn, Variational principles for circle patterns and Koebe’s theorem, Trans. Amer. Math. Soc. 356 (2004) 659 MR2022715
7 A I Bobenko, Y B Suris, Discrete differential geometry: integrable structure, 98, Amer. Math. Soc. (2008) MR2467378
8 V Fock, Description of moduli space of projective structures via fat graphs, preprint (1993) arXiv:hep-th/9312193
9 V Fock, A Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. 103 (2006) 1 MR2233852
10 X Gu, R Guo, F Luo, J Sun, T Wu, A discrete uniformization theorem for polyhedral surfaces, II, J. Differential Geom. 109 (2018) 431 MR3825607
11 R C Gunning, Lectures on Riemann surfaces, Princeton Univ. Press (1966) MR0207977
12 Z X He, Solving Beltrami equations by circle packing, Trans. Amer. Math. Soc. 322 (1990) 657 MR974518
13 B Jessen, Orthogonal icosahedra, Nordisk Mat. Tidskr. 15 (1967) 90 MR226494
14 R Kenyon, W Y Lam, S Ramassamy, M Russkikh, Dimers and circle patterns, preprint (2018) arXiv:1810.05616
15 L Kharevych, B Springborn, P Schröder, Discrete conformal mappings via circle patterns, ACM Trans. Graph. 25 (2006) 412
16 S Kojima, S Mizushima, S P Tan, Circle packings on surfaces with projective structures, J. Differential Geom. 63 (2003) 349 MR2015468
17 W Y Lam, Discrete minimal surfaces: critical points of the area functional from integrable systems, Int. Math. Res. Not. 2018 (2018) 1808 MR3800636
18 W Y Lam, Minimal surfaces from infinitesimal deformations of circle packings, Adv. Math. 362 (2020) MR4046071
19 W Y Lam, U Pinkall, Holomorphic vector fields and quadratic differentials on planar triangular meshes, from: "Advances in discrete differential geometry" (editor A I Bobenko), Springer (2016) 241 MR3587188
20 W Y Lam, U Pinkall, Isothermic triangulated surfaces, Math. Ann. 368 (2017) 165 MR3651570
21 F Loray, D Marín Pérez, Projective structures and projective bundles over compact Riemann surfaces, from: "Équations différentielles et singularités" (editors F Cano, F Loray, J J Moralez-Ruiz, P Sad, M Spivakovsky), Astérisque 323, Soc. Math. France (2009) 223 MR2647972
22 S Mizushima, Circle packings on complex affine tori, Osaka J. Math. 37 (2000) 873 MR1809910
23 U Pinkall, K Polthier, Computing discrete minimal surfaces and their conjugates, Experiment. Math. 2 (1993) 15 MR1246481
24 I Rivin, Euclidean structures on simplicial surfaces and hyperbolic volume, Ann. of Math. 139 (1994) 553 MR1283870
25 B Rodin, D Sullivan, The convergence of circle packings to the Riemann mapping, J. Differential Geom. 26 (1987) 349 MR906396
26 C T Sass, K Stephenson, G B Williams, Circle packings on conformal and affine tori, from: "Computational algebraic and analytic geometry" (editors M Seppälä, E Volcheck), Contemp. Math. 572, Amer. Math. Soc. (2012) 211 MR2953831
27 J M Schlenker, A Yarmola, Properness for circle packings and Delaunay circle patterns on complex projective structures, preprint (2018) arXiv:1806.05254
28 S Smirnov, Discrete complex analysis and probability, from: "Proceedings of the International Congress of Mathematicians, I" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan), Hindustan (2010) 595 MR2827906
29 K Stephenson, Introduction to circle packing: the theory of discrete analytic functions, Cambridge Univ. Press (2005) MR2131318
30 W P Thurston, The geometry and topology of 3–manifolds, lecture notes (1980)
31 G B Williams, Constructing quasiconformal maps using circle packings and Brook’s parametrization of quadrilaterals, Ann. Acad. Sci. Fenn. Math. 44 (2019) 877 MR3973545