Des immersions isométriques de surfaces aux variétés hyperboliques à bord convexe
Séminaire de théorie spectrale et géométrie (2002-2003)
- Volume: 21, page 165-216
- ISSN: 1624-5458
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topSchlenker, Jean-Marc. "Des immersions isométriques de surfaces aux variétés hyperboliques à bord convexe." Séminaire de théorie spectrale et géométrie 21 (2002-2003): 165-216. <http://eudml.org/doc/114473>.
@article{Schlenker2002-2003,
author = {Schlenker, Jean-Marc},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {anti-de Sitter manifold; hyperbolic manifold with convex boundary; isometric immersion},
language = {fre},
pages = {165-216},
publisher = {Institut Fourier},
title = {Des immersions isométriques de surfaces aux variétés hyperboliques à bord convexe},
url = {http://eudml.org/doc/114473},
volume = {21},
year = {2002-2003},
}
TY - JOUR
AU - Schlenker, Jean-Marc
TI - Des immersions isométriques de surfaces aux variétés hyperboliques à bord convexe
JO - Séminaire de théorie spectrale et géométrie
PY - 2002-2003
PB - Institut Fourier
VL - 21
SP - 165
EP - 216
LA - fre
KW - anti-de Sitter manifold; hyperbolic manifold with convex boundary; isometric immersion
UR - http://eudml.org/doc/114473
ER -
References
top- [Ale58a] A.D. ALEKSANDROV, Vestnik Leningrad Univ., 13(1), 1958.
- [Ale58b] A.D. ALEXANDROW, Konvexe polyeder. Akademie-Verlag, Berlin, 1958. MR92989
- [And70] E.M. ANDREEV, Convex polyhedra in Lobacevskii space. Mat. Sb. (N.S.), 81 (123):445-478, 1970. Zbl0194.23202MR259734
- [And71] E.M. ANDREEV, On convex polyhedra of finite volume in Lobacevskii space. Math. USSR Sbornik, 12 (3):225-259, 1971. Zbl0252.52005MR273510
- [BB02] X. BAO and F. BONAHON, Hyperideal polyhedra in hyperbolic 3 space. Preprint available at http://math.usc.edu/~fbonahon. Bull. Soc. Math. France, to appear, 2002. Zbl1033.52009MR1943885
- [BC03] M. BRIDGEMAN and R.-D. CANARY, From the boundary of the convex core to the conformal boun dary. Geom. Dedicata, 96:211-240, 2003. Zbl1083.57024MR1956842
- [BO01] F. BONAHON and J.-P. OTAL, Laminations mesurées de plissage des variétés hyperboliques de dimension 3. http://math.usc.edu/~fbonahon, 2001. Zbl1083.57023
- [Bon96] F. BONAHON, Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form. Ann. Fac. Sci. Toulouse Math. (6), 5(2):233-297, 1996. Zbl0880.57005MR1413855
- [Bon01] F. BONAHON, Geodesic laminations on surfaces. In Laminations and foliations in dynamics, geometry and topology (Stony Brook, NY, 1998), volume 269 of Contemp. Math., pages 1-37. Amer. Math. Soc, Providence, RI, 2001. Zbl0996.53029MR1810534
- [Brä92] W. BRÄGGER, Kreispackungen und Triangulierungen. Enseign. Math. (2), 38(3-4):201-217, 1992. Zbl0770.52007MR1189006
- [Cal61] E. CALABI, On compact Riemannian manifolds with constant curvature, I. AMS proceedings of Symposia in Pure Math, 3:155-180, 1961. Zbl0129.14102MR133787
- [Cau13] A.L. CAUCHY, Sur les polygones et polyèdres, second mémoire. Journal de l'Ecole Polytechnique, 19:87-98, 1813.
- [CdV91] Y. COLIN DE VERDIÈRE, Un principe variationnel pour les empilements de cercles. Invent. Math., 104(3):655-669, 1991. Zbl0745.52010MR1106755
- [EM86] D.B.A. EPSTEIN and A. MARDEN, Convex hulls in hyperbolic spaces, a theorem of Sullivan, and measured pleated surfaces. In D.B.A. Epstein, editor, Analytical and geometric aspects of hyperbolic space, volume 111 of L.M.S. Lecture Note Series. Cambridge University Press, 1986. Zbl0612.57010
- [Fil] F. FILLASTRE, Surfaces convexes fuchsiennes. In preparation.
- [Gro85] M. GROMOV, Pseudo-holomorphic curves in symplectic manifolds. Inventiones Math., 82:307-347, 1985. Zbl0592.53025
- [Gro86] M. GROMOV, Partial Differential Relations. Springer, 1986. Zbl0651.53001MR864505
- [HK98] C.D. HODGSON and S.P. KERCKHOFF, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery. J. Differential Geom., 48:1-60, 1998. Zbl0919.57009MR1622600
- [Isk00] I. ISKHAKOV, On hyperbolic surface tessellations and equivariant spacelike convex polyhedral surfaces in Minkowski space. PhD thesis, Ohio State University, 2000.
- [Koe36] P. KOEBE, Kontaktprobleme der konformen Abbildung. Abh. Sächs. Akad. Wiss. Leipzig Math.-Natur. Kl., 88:141-164, 1936. JFM62.1217.04
- [Lab89] F. LABOURIE, Immersions isométriques elliptiques et courbes pseudo-holomorphes. J. Differential Geom., 30:395-424, 1989. Zbl0682.53063MR1010166
- [Lab92] F. LABOURIE, Métriques prescrites sur le bord des variétés hyperboliques de dimension 3. J. Differential Geom., 35:609-626, 1992. Zbl0768.53017MR1163450
- [Lab94] F. LABOURIE, Exemples de courbes pseudo-holomorphes en géométrie riemannienne. In Audin and Lafontaine, editors, Pseudo-Holomorphic Curves in Symplectic Geometry, pages 251-270. Birkhauser, 1994. MR1274933
- [Lab97] F. LABOURIE, Problèmes de Monge-Ampère, courbes holomorphes et laminations. Geom. Funct. Anal., 7(3):496-534, 1997. Zbl0885.32013MR1466336
- [Lab 00] F. LABOURIE, Un lemme de Morse pour les surfaces convexes. Invent. Math., 141 (2):239-297, 2000. Zbl0981.52002MR1775215
- [LecO2] C. LECUIRE, Plissage des variétés hyperboliques de dimension 3. Preprint 301, UMPA, ENS Lyon, 2002. MR2207784
- [LegII] A.-M. LEGENDRE, Eléments de géométrie. Paris, 1793 (an II). Première édition, note XII, pp. 321-334.
- [LS00] F. LABOURIE and J.-M. SCHLENKER, Surfaces convexes fuchsiennes dans les espaces lorentziens à courbure constante. Math. Annalen, 316:465-483, 2000. Zbl0968.53047MR1752780
- [Mes90] G. MESS, Lorentz spacetimes of constant curvature. Preprint I.H.E.S./M/90/28, 1990. MR2328921
- [Mou02] G. MOUSSONG, Personal communication. July 2002.
- [Pog73] A.V. POGORELOV, Extrinsic Geometry of Convex Surfaces. American Mathematical Society, 1973. Translations of Mathematical Monographs. Vol.35. Zbl0311.53067MR346714
- [RH93] I. RIVIN and C. D. HODGSON, A characterization of compact convex polyhedra in hyperbolic 3-space. Invent.Math., 111:77-111, 1993. Zbl0784.52013MR1193599
- [Riv86] I. RIVIN, Thesis. PhD thesis, Princeton University, 1986.
- [Riv92] I. RIVIN, Intrinsic geometry of convex ideal polyhedra in hyperbolic 3-space. In M. Gyllenberg and L. E. Persson, editors, Analysis, Algebra, and Computers in Mathematical Research, pages 275-292. Marcel Dekker, 1992. (Proc. of the 21 st Nordic Congress of Mathematicians). Zbl0823.52008MR1280952
- [Riv94] I. RIVIN, Euclidean structures on simplicial surfaces and hyperbolic volume. Annals of Math., 139:553-580, 1994. Zbl0823.52009MR1283870
- [Riv96] I. RIVIN, A characterization of ideal polyhedra in hyperbolic 3-space. Annals of Math., 143:51-70, 1996. Zbl0874.52006MR1370757
- [Rou02] M. ROUSSET, Sur la rigidité de polyèdres hyperboliques en dimension 3 : cas de volume fini, cas hyperidéal, cas fuchsien. math.GT/0211280; Bull. Soc. Math. France, to appear, 2002. Zbl1061.52007MR2075567
- [Sch96] J.-M. SCHLENKER, Surfaces convexes dans des espaces lorentziens à courbure constante. Commun. Anal, and Geom., 4:285-331, 1996. Zbl0864.53016MR1393565
- [Sch98a] J.-M. SCHLENKER, Métriques sur les polyèdres hyperboliques convexes. J. Differential Geom., 48 (2) :323-405, 1998. Zbl0912.52008MR1630178
- [Sch98b] J.-M. SCHLENKER, Représentations de surfaces hyperboliques complètes dans H3. Annales de l'Institut Fourier, 48 (3):837-860, 1998. Zbl0916.53029MR1644101
- [Sch00] J.-M. SCHLENKER, Dihedral angles of convex polyhedra. Discrete Comput. Geom., 23 (3):409-417, 2000. Zbl0951.52006MR1744513
- [Sch01a] textsc J.-M. Schlenker, Convex polyhedra in Lorentzian space-forms. Asian J. of Math., 5: 327-364, 2001. Zbl1020.53046MR1868937
- [Sch01b] J.-M. SCHLENKER, Einstein manifolds with convex boundaries. Commentarii Math. Helvetici, 76(l) :l-28, 2001. Zbl1036.53031MR1819659
- [Sch01c] J.-M. SCHLENKER, Hyperbolic manifolds with polyhedral boundary. math. GT/0111136, available at http://picard.ups-tlse.fr/-schlenker, 2001.
- [Sch02a] J.-M. SCHLENKER, Hyperbolic manifolds with convex boundary. preprint, math. DG/0205305, available at http://picard.ups-tlse.fr/-schlenker, 2002. MR2208419
- [Sch02b] J.-M. SCHLENKER, Hyperideal polyhedra in hyperbolic manifolds. Preprint math. GT/0212355., 2002.
- [Sch03] J.-M. SCHLENKER, Hyperbolic manifolds with constant curvature boundaries. In preparation, 2003.
- [Sul79] D. SULLIVAN, The density at infinity of a discrete group of hyperbolic motions. Inst. Hautes Études Sci. Publ Math., (50):171-202, 1979. Zbl0439.30034MR556586
- [Thu97] W.-P. THURSTON, Three-dimensional geometry and topology. Recent version of the 1980 notes. http://wvwv.msri.org/publications/books/gt3m/, 1997. Zbl0873.57001
- [Tro91] M. TROYANOVPrescribing curvature on compact surfaces with conical singularities. Trans. Amer. Math. Soc, 324(2):793-821, 1991. Zbl0724.53023MR1005085
- [Wei60] A. WEIL, On discrete subgroups of Lie groups. Annals of Math., 72(l):369-384, 1960. Zbl0131.26602MR137792
- [Wei02] H. WEISS, Local rigidity of 3-dimensional cone-manifolds. PhD thesis, available at http://www.mathematik.uni-muenchen. de/personen/weiss.html, 2002.
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