Geometry & Topology Volume 26, issue 3 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Combinatorial Ricci flows and the hyperbolization of a class of compact $3$–manifolds

Ke Feng, Huabin Ge and Bobo Hua

Geometry & Topology 26 (2022) 1349–1384

DOI: 10.2140/gt.2022.26.1349

Bibliography

1	X Bao, F Bonahon, Hyperideal polyhedra in hyperbolic 3–space, Bull. Soc. Math. France 130 (2002) 457 MR1943885
2	A I Bobenko, U Pinkall, B A Springborn, Discrete conformal maps and ideal hyperbolic polyhedra, Geom. Topol. 19 (2015) 2155 MR3375525
3	F Bonahon, A Schläfli-type formula for convex cores of hyperbolic 3–manifolds, J. Differential Geom. 50 (1998) 25 MR1678473
4	Y E Choi, Positively oriented ideal triangulations on hyperbolic three-manifolds, Topology 43 (2004) 1345 MR2081429
5	B Chow, F Luo, Combinatorial Ricci flows on surfaces, J. Differential Geom. 63 (2003) 97 MR2015261
6	H Cohn, R Kenyon, J Propp, A variational principle for domino tilings, J. Amer. Math. Soc. 14 (2001) 297 MR1815214
7	Y Colin de Verdière, Un principe variationnel pour les empilements de cercles, Invent. Math. 104 (1991) 655 MR1106755
8	F Costantino, R Frigerio, B Martelli, C Petronio, Triangulations of 3–manifolds, hyperbolic relative handlebodies, and Dehn filling, Comment. Math. Helv. 82 (2007) 903 MR2341844
9	F Costantino, F Guéritaud, R van der Veen, On the volume conjecture for polyhedra, Geom. Dedicata 179 (2015) 385 MR3424676
10	R Frigerio, Hyperbolic manifolds with geodesic boundary which are determined by their fundamental group, Topology Appl. 145 (2004) 69 MR2100865
11	R Frigerio, C Petronio, Construction and recognition of hyperbolic 3–manifolds with geodesic boundary, Trans. Amer. Math. Soc. 356 (2004) 3243 MR2052949
12	M Fujii, Hyperbolic 3–manifolds with totally geodesic boundary, Osaka J. Math. 27 (1990) 539 MR1075164
13	M Fujii, Hyperbolic 3–manifolds with totally geodesic boundary which are decomposed into hyperbolic truncated tetrahedra, Tokyo J. Math. 13 (1990) 353 MR1088237
14	D Futer, F Guéritaud, From angled triangulations to hyperbolic structures, from: "Interactions between hyperbolic geometry, quantum topology and number theory" (editors A Champanerkar, O Dasbach, E Kalfagianni, I Kofman, W Neumann, N Stoltzfus), Contemp. Math. 541, Amer. Math. Soc. (2011) 159 MR2796632
15	S Garoufalidis, C D Hodgson, J H Rubinstein, H Segerman, 1–efficient triangulations and the index of a cusped hyperbolic 3–manifold, Geom. Topol. 19 (2015) 2619 MR3416111
16	H Ge, B Hua, 3–Dimensional combinatorial Yamabe flow in hyperbolic background geometry, Trans. Amer. Math. Soc. 373 (2020) 5111 MR4127872
17	H Ge, W Jiang, On the deformation of discrete conformal factors on surfaces, Calc. Var. Partial Differential Equations 55 (2016) MR3566936
18	H Ge, W Jiang, L Shen, On the deformation of ball packings, Adv. Math. 398 (2022) MR4367796
19	C D Hodgson, J H Rubinstein, H Segerman, Triangulations of hyperbolic 3–manifolds admitting strict angle structures, J. Topol. 5 (2012) 887 MR3001314
20	M Kapovich, Hyperbolic manifolds and discrete groups, 183, Birkhäuser (2001) MR1792613
21	S Kojima, Polyhedral decomposition of hyperbolic 3–manifolds with totally geodesic boundary, from: "Aspects of low-dimensional manifolds" (editors Y Matsumoto, S Morita), Adv. Stud. Pure Math. 20, Kinokuniya (1992) 93 MR1208308
22	M Lackenby, Taut ideal triangulations of 3–manifolds, Geom. Topol. 4 (2000) 369 MR1790190
23	M Lackenby, Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243 MR1756996
24	D D Long, A W Reid, Constructing hyperbolic manifolds which bound geometrically, Math. Res. Lett. 8 (2001) 443 MR1849261
25	F Luo, A combinatorial curvature flow for compact 3–manifolds with boundary, Electron. Res. Announc. Amer. Math. Soc. 11 (2005) 12 MR2122445
26	F Luo, Volume and angle structures on 3–manifolds, Asian J. Math. 11 (2007) 555 MR2402938
27	F Luo, Rigidity of polyhedral surfaces, III, Geom. Topol. 15 (2011) 2299 MR2862158
28	F Luo, Volume optimization, normal surfaces, and Thurston’s equation on triangulated 3–manifolds, J. Differential Geom. 93 (2013) 299 MR3024308
29	F Luo, T Yang, Volume and rigidity of hyperbolic polyhedral 3–manifolds, J. Topol. 11 (2018) 1 MR3747038
30	E E Moise, Affine structures in 3–manifolds, V : The triangulation theorem and Hauptvermutung, Ann. of Math. 56 (1952) 96 MR48805
31	J P Otal, Le théorème d’hyperbolisation pour les variétés fibrées de dimension 3, 235, Soc. Math. France (1996) MR1402300
32	L S Pontryagin, Ordinary differential equations, Addison-Wesley (1962) MR0140742
33	I Rivin, Euclidean structures on simplicial surfaces and hyperbolic volume, Ann. of Math. 139 (1994) 553 MR1283870
34	I Rivin, Combinatorial optimization in geometry, Adv. Appl. Math. 31 (2003) 242 MR1985831
35	I Rivin, Volumes of degenerating polyhedra : on a conjecture of J W Milnor, Geom. Dedicata 131 (2008) 73 MR2369192
36	J M Schlenker, Hyperideal polyhedra in hyperbolic manifolds, preprint (2002) arXiv:math/0212355
37	W Thurston, Geometry and topology of three-manifolds, lecture notes (1980)
38	A Ushijima, A volume formula for generalised hyperbolic tetrahedra, from: "Non-Euclidean geometries" (editors A Prékopa, E Molnár), Math. Appl. (NY) 581, Springer (2006) 249 MR2191251
39	H Weiss, The deformation theory of hyperbolic cone-3–manifolds with cone-angles less than 2π, Geom. Topol. 17 (2013) 329 MR3035330