[Polyèdres hyperidéaux de l’espace hyperbolique de dimension
Un polyèdre hyperidéal est un polyèdre non-compact de l’espace hyperbolique
A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic
Keywords: hyperbolic space, polyhedron, ideal polyhedron, hyperideal
Mot clés : espace hyperbolique, polyèdre, polyèdre idéal, hyperidéal
@article{BSMF_2002__130_3_457_0, author = {Bao, Xiliang and Bonahon, Francis}, title = {Hyperideal polyhedra in hyperbolic 3-space}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {457--491}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {130}, number = {3}, year = {2002}, doi = {10.24033/bsmf.2426}, mrnumber = {1943885}, zbl = {1033.52009}, language = {en}, url = {http://www.numdam.org/articles/10.24033/bsmf.2426/} }
TY - JOUR AU - Bao, Xiliang AU - Bonahon, Francis TI - Hyperideal polyhedra in hyperbolic 3-space JO - Bulletin de la Société Mathématique de France PY - 2002 SP - 457 EP - 491 VL - 130 IS - 3 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/bsmf.2426/ DO - 10.24033/bsmf.2426 LA - en ID - BSMF_2002__130_3_457_0 ER -
%0 Journal Article %A Bao, Xiliang %A Bonahon, Francis %T Hyperideal polyhedra in hyperbolic 3-space %J Bulletin de la Société Mathématique de France %D 2002 %P 457-491 %V 130 %N 3 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/bsmf.2426/ %R 10.24033/bsmf.2426 %G en %F BSMF_2002__130_3_457_0
Bao, Xiliang; Bonahon, Francis. Hyperideal polyhedra in hyperbolic 3-space. Bulletin de la Société Mathématique de France, Tome 130 (2002) no. 3, pp. 457-491. doi : 10.24033/bsmf.2426. http://www.numdam.org/articles/10.24033/bsmf.2426/
[1] Konvexe Polyeder, Akademie-Verlag, Berlin, 1958. | MR
-[2] « On Convex Polyhedra in Lobačevskiĭ Spaces (Russian) », Mat. Sbornik 81 (123) (1970), p. 445-478; English transl., Math. USSR Sb. t.10 (1970), pp.413-440. | MR | Zbl
-[3] -, « On Convex Polyhedra of Finite Volume in Lobačevskiĭ Spaces (Russian) », Mat. Sbornik 83 (125) (1970), p. 256-260; English transl., Math. USSR Sb. t.12 (1970), pp.255-259. | MR | Zbl
[4] Hyperideal Polyhedra in Hyperbolic
[5] « Sur les polygones et les polyèdres », J. École Polytechnique 9 (1813), p. 87-98.
-[6] « On Complexes with Transitive Groups of Automorphisms », Ann. of Math. 35 (1934), p. 588-621. | JFM | Zbl
-[7] Polyhedra, Cambridge University Press, 1997. | MR | Zbl
-[8] Convex Polytopes, Interscience Publishers, John Wiley & Sons Inc., New York, 1967. | MR | Zbl
-[9] A Course in Combinatorics, Cambridge University Press, 1992. | MR | Zbl
& -[10] « Euclidean Structures on Simplicial Surfaces and Hyperbolic Volume », Ann. of Math. 139 (1994), p. 553-580. | MR | Zbl
-
[11] -, « A Characterization of Ideal Polyhedra in Hyperbolic
[12] « A Characterization of Compact Convex Polyhedra in Hyperbolic
[13] « Métriques sur les polyèdres hyperboliques convexes », J. Diff. Geom. 48 (1998), p. 323-405. | MR | Zbl
-[14] -, « Dihedral Angles of Convex Polyhedra », Discrete Comp. Geom. 23 (2000), p. 409-417. | MR | Zbl
[15] « Geometrical Problems Concerning Polyhedra in the Large », Comm. Pure Appl. Math. 21 (1958), p. 119-168. | MR | Zbl
-[16] Three-Dimensional Geometry and Topology, (S. Levy, ed.), Princeton Math. Series, vol. 35, Princeton University Press, 1997. | MR | Zbl
-[17] « Discrete groups generated by reflections in Lobačevskiĭ spaces », Mat. Sbornik 72 (114) (1967), p. 471-488; English transl., Math. USSR Sb. t.1 (1967), pp.429-444; Correction, Mat. Sbornik t.73 (115) (1967), pp.303. | MR | Zbl
-- Adjoint twisted Reidemeister torsion and Gram matrices, Advances in Mathematics, Volume 438 (2024), p. 45 (Id/No 109470) | DOI:10.1016/j.aim.2023.109470 | Zbl:7801738
- The character of Thurston's circle packings, Science China. Mathematics, Volume 67 (2024) no. 7, pp. 1623-1640 | DOI:10.1007/s11425-023-2182-2 | Zbl:1544.52012
- Upper bounds for volumes of generalized hyperbolic polyhedra and hyperbolic links, Siberian Mathematical Journal, Volume 65 (2024) no. 3, pp. 534-551 | DOI:10.1134/s0037446624030042 | Zbl:7918227
- The volume conjecture for polyhedra implies the Stoker conjecture, Geometriae Dedicata, Volume 217 (2023) no. 4, p. 10 (Id/No 77) | DOI:10.1007/s10711-023-00813-y | Zbl:1528.57022
- A relative version of the Turaev-Viro invariants and the volume of hyperbolic polyhedral 3-manifolds, Journal of Topology, Volume 16 (2023) no. 2, pp. 650-678 | DOI:10.1112/topo.12300 | Zbl:1542.57012
- Hyperideal polyhedra in the 3-dimensional anti-de Sitter space, Advances in Mathematics, Volume 404 (2022), p. 61 (Id/No 108441) | DOI:10.1016/j.aim.2022.108441 | Zbl:1494.52009
- Irreducible metric maps and Weil-Petersson volumes, Communications in Mathematical Physics, Volume 394 (2022) no. 2, pp. 887-917 | DOI:10.1007/s00220-022-04418-6 | Zbl:1495.05061
- Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds, Geometry Topology, Volume 26 (2022) no. 3, pp. 1349-1384 | DOI:10.2140/gt.2022.26.1349 | Zbl:1505.57025
- Growth of quantum
-symbols and applications to the volume conjecture, Journal of Differential Geometry, Volume 120 (2022) no. 2, pp. 199-229 | DOI:10.4310/jdg/1645207506 | Zbl:1493.57012 - Combinatorial Ricci flow on compact 3-manifolds with boundary, Journal of Functional Analysis, Volume 283 (2022) no. 5, p. 19 (Id/No 109556) | DOI:10.1016/j.jfa.2022.109556 | Zbl:1497.53145
- Asymptotic additivity of the Turaev–Viro invariants for a family of 3‐manifolds, Journal of the London Mathematical Society, Volume 106 (2022) no. 4, p. 3043 | DOI:10.1112/jlms.12655
- Combinatorial Ricci flows for ideal circle patterns, Advances in Mathematics, Volume 383 (2021), p. 26 (Id/No 107698) | DOI:10.1016/j.aim.2021.107698 | Zbl:1464.52014
- Combinatorial Calabi flow on 3-manifolds with toroidal boundary, Journal of Functional Analysis, Volume 280 (2021) no. 11, p. 23 (Id/No 108990) | DOI:10.1016/j.jfa.2021.108990 | Zbl:1465.53101
- The maximum volume of hyperbolic polyhedra, Transactions of the American Mathematical Society, Volume 374 (2021) no. 2, pp. 1125-1153 | DOI:10.1090/tran/8215 | Zbl:1456.52015
- Ideal hyperbolic polyhedra and discrete uniformization, Discrete Computational Geometry, Volume 64 (2020) no. 1, pp. 63-108 | DOI:10.1007/s00454-019-00132-8 | Zbl:1518.30015
- Combinatorics encoding geometry: the legacy of Bill Thurston in the story of one theorem, In the tradition of Thurston. Geometry and topology, Cham: Springer, 2020, pp. 173-239 | DOI:10.1007/978-3-030-55928-1_5 | Zbl:1486.52055
- Polyhedra inscribed in a quadric, Inventiones Mathematicae, Volume 221 (2020) no. 1, pp. 237-300 | DOI:10.1007/s00222-020-00948-9 | Zbl:1441.52011
- Rigidity of circle polyhedra in the 2-sphere and of hyperideal polyhedra in hyperbolic 3-space, Transactions of the American Mathematical Society, Volume 371 (2019) no. 6, pp. 4215-4249 | DOI:10.1090/tran/7483 | Zbl:1414.52015
- Volume and rigidity of hyperbolic polyhedral 3-manifolds, Journal of Topology, Volume 11 (2018) no. 1, pp. 1-29 | DOI:10.1112/topo.12046 | Zbl:1398.57032
- Discrete uniformization of polyhedral surfaces with non-positive curvature and branched covers over the sphere via hyper-ideal circle patterns, Discrete Computational Geometry, Volume 57 (2017) no. 2, pp. 431-469 | DOI:10.1007/s00454-016-9830-2 | Zbl:1365.52027
- Scribability problems for polytopes, European Journal of Combinatorics, Volume 64 (2017), pp. 1-26 | DOI:10.1016/j.ejc.2017.02.006 | Zbl:1370.52017
- Intersection number and stability of some inscribable graphs, Geometriae Dedicata, Volume 185 (2016), pp. 105-121 | DOI:10.1007/s10711-016-0170-4 | Zbl:1359.52006
- How many cages midscribe an egg, Inventiones Mathematicae, Volume 203 (2016) no. 2, pp. 655-673 | DOI:10.1007/s00222-015-0602-z | Zbl:1339.52010
- On the volume conjecture for polyhedra, Geometriae Dedicata, Volume 179 (2015), pp. 385-409 | DOI:10.1007/s10711-015-0086-4 | Zbl:1336.57029
- Hyper-ideal circle patterns with cone singularities, Results in Mathematics, Volume 68 (2015) no. 3-4, pp. 455-499 | DOI:10.1007/s00025-015-0453-3 | Zbl:1330.52026
- (ℤ2)3-colorings and right-angled hyperbolic 3-manifolds, Pacific Journal of Mathematics, Volume 263 (2013) no. 2, p. 419 | DOI:10.2140/pjm.2013.263.419
- Bending invariants of poly-circles. I: Rigidity, Geometriae Dedicata, Volume 150 (2011), pp. 281-305 | DOI:10.1007/s10711-010-9507-6 | Zbl:1226.51007
- Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra, Geometriae Dedicata, Volume 153 (2011), pp. 177-211 | DOI:10.1007/s10711-010-9563-y | Zbl:1241.57022
- Circle patterns on singular surfaces, Discrete Computational Geometry, Volume 40 (2008) no. 1, pp. 47-102 | DOI:10.1007/s00454-007-9045-7 | Zbl:1191.52013
- Polyhedral hyperbolic metrics on surfaces, Geometriae Dedicata, Volume 134 (2008), pp. 177-196 | DOI:10.1007/s10711-008-9252-2 | Zbl:1153.57012
- A variational principle for weighted Delaunay triangulations and hyperideal polyhedra, Journal of Differential Geometry, Volume 78 (2008) no. 2, pp. 333-367 | DOI:10.4310/jdg/1203000270 | Zbl:1181.52018
- Andreev's theorem on hyperbolic polyhedra, Annales de l'Institut Fourier, Volume 57 (2007) no. 3, pp. 825-882 | DOI:10.5802/aif.2279 | Zbl:1127.51012
- Finite simultaneous bending, Conformal Geometry and Dynamics, Volume 10 (2006), pp. 203-226 | DOI:10.1090/s1088-4173-06-00119-6 | Zbl:1112.52009
- Hyperbolic manifolds with convex boundary, Inventiones Mathematicae, Volume 163 (2006) no. 1, pp. 109-169 | DOI:10.1007/s00222-005-0456-x | Zbl:1091.53019
- A combinatorial curvature flow for compact 3-manifolds with boundary, Electronic Research Announcements of the American Mathematical Society, Volume 11 (2005), pp. 12-20 | DOI:10.1090/s1079-6762-05-00142-3 | Zbl:1079.53098
Cité par 35 documents. Sources : Crossref, zbMATH