Geometry & Topology Volume 13, issue 1 (2009)

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

Hyperbolic cusps with convex polyhedral boundary

François Fillastre and Ivan Izmestiev

Geometry & Topology 13 (2009) 457–492

DOI: 10.2140/gt.2009.13.457

Bibliography

1	A Alexandroff, Existence of a convex polyhedron and of a convex surface with a given metric, Rec. Math. [Mat. Sbornik] N.S. 11(53) (1942) 15 MR0013540
2	A D Alexandrov, Convex polyhedra, Springer Monographs in Math., Springer (2005) MR2127379
3	M T Anderson, Scalar curvature and the existence of geometric structures on $3$–manifolds. I, J. Reine Angew. Math. 553 (2002) 125 MR1944810
4	E M Andreev, Convex polyhedra in Lobačevskiĭspaces, Mat. Sb. $($N.S.$)$ 81 (123) (1970) 445 MR0259734
5	W Blaschke, G Herglotz, Über die Verwirklichung einer geschlossenen Fläche mit vorgeschriebenem Bogenelement im Euklidischen Raum, Sitzungsber. Bayer. Akad. Wiss., Math.-Naturwiss. Abt. 2 (1937) 229
6	A I Bobenko, I Izmestiev, Alexandrov's theorem, weighted Delaunay triangulations, and mixed volumes, Ann. Inst. Fourier (Grenoble) 58 (2008) 447 MR2410380
7	F Bonsante, J M Schlenker, AdS manifolds with particles and earthquakes on singular surfaces, To appear in Geom. Funct. Anal. arXiv:math/0609116
8	R D Canary, D B A Epstein, P L Green, Notes on notes of Thurston [MR0903850], from: "Fundamentals of hyperbolic geometry: selected expositions", London Math. Soc. Lecture Note Ser. 328, Cambridge Univ. Press (2006) 1 MR2235710
9	A L Cauchy, Sur les polygones et polyèdres (Second Mémoire), from: "\OEvres complètes, Seconde série 1" (1905) 26
10	R Connelly, J M Schlenker, On the infinitesimal rigidity of weakly convex polyhedra arXiv:math/0606681
11	F Fillastre, Fuchsian polyhedra in Lorentzian space-forms arXiv:math.DG/0702532
12	F Fillastre, Polyhedral realisation of hyperbolic metrics with conical singularities on compact surfaces, Ann. Inst. Fourier (Grenoble) 57 (2007) 163 MR2313089
13	F Fillastre, Polyhedral hyperbolic metrics on surfaces, Geom. Dedicata 134 (2008) 177 MR2399657
14	F Fillastre, I Izmestiev, Dual metrics of hyperbolic cusps with convex polyhedral boundary, In preparation (2008)
15	C D Hodgson, Deduction of Andreev's theorem from Rivin's characterization of convex hyperbolic polyhedra, from: "Topology '90 (Columbus, OH, 1990)", Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 185 MR1184410
16	C D Hodgson, I Rivin, A characterization of compact convex polyhedra in hyperbolic $3$–space, Invent. Math. 111 (1993) 77 MR1193599
17	C Indermitte, T M Liebling, M Troyanov, H Clémençon, Voronoi diagrams on piecewise flat surfaces and an application to biological growth, from: "Combinatorics and computer science (Palaiseau, 1997)", Theoret. Comput. Sci. 1-2 (2001) 263 MR1846934
18	I Izmestiev, A variational proof of Alexandrov's convex cap theorem, To appear in Discrete Comput. Geom. arXiv:math/0703169
19	K Krasnov, J M Schlenker, Minimal surfaces and particles in $3$–manifolds, Geom. Dedicata 126 (2007) 187 MR2328927
20	F Labourie, J M Schlenker, Surfaces convexes fuchsiennes dans les espaces lorentziens à courbure constante, Math. Ann. 316 (2000) 465 MR1752780
21	F Luo, Rigidity of polyhedral surfaces arXiv:math.GT/0612714
22	J Milnor, Collected papers. Vol. 1. Geometry, Publish or Perish (1994) MR1277810
23	S Moroianu, J M Schlenker, Quasi-Fuchsian manifolds with particles arXiv:math/0603441
24	I Rivin, On geometry of convex polyhedra in hyperbolic $3$–space, PhD thesis, Princeton University (1986)
25	I Rivin, Euclidean structures on simplicial surfaces and hyperbolic volume, Ann. of Math. $(2)$ 139 (1994) 553 MR1283870
26	J M Schlenker, Hyperbolic manifolds with polyhedral boundary
27	J M Schlenker, On weakly convex star-shaped polyhedra arXiv:0704.2901
28	J M Schlenker, Surfaces convexes dans des espaces lorentziens à courbure constante, Comm. Anal. Geom. 4 (1996) 285 MR1393565
29	J M Schlenker, Convex polyhedra in Lorentzian space-forms, Asian J. Math. 5 (2001) 327 MR1868937
30	J M Schlenker, Hyperbolic manifolds with convex boundary, Invent. Math. 163 (2006) 109 MR2208419
31	S Sechelmann, Alexandrov polyhedron editor
32	W P Thurston, Shapes of polyhedra and triangulations of the sphere, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1 (1998) 511 MR1668340
33	Y A Volkov, Existence of a polyhedron with a given development, PhD thesis, Leningrad State University (1955)
34	Y A Volkov, Existence of convex polyhedra with prescribed development I, Vestn. Leningr. Univ. 15 (1960) 75