Schlenker, Jean-Marc
Des immersions isométriques de surfaces aux variétés hyperboliques à bord convexe
Séminaire de théorie spectrale et géométrie, Tome 21 (2002-2003) , p. 165-216
Zbl 1059.53055 | MR 2052831
URL stable : http://www.numdam.org/item?id=TSG_2002-2003__21__165_0

Bibliographie

[Ale58a] A.D. Aleksandrov, Vestnik Leningrad Univ., 13(1), 1958.

[Ale58b] A.D. Alexandrow, Konvexe polyeder. Akademie-Verlag, Berlin, 1958. MR 92989

[And70] E.M. Andreev, Convex polyhedra in Lobacevskii space. Mat. Sb. (N.S.), 81 (123):445-478, 1970. MR 259734 | Zbl 0194.23202

[And71] E.M. Andreev, On convex polyhedra of finite volume in Lobacevskii space. Math. USSR Sbornik, 12 (3):225-259, 1971. MR 273510 | Zbl 0252.52005

[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. Numdam | MR 1943885 | Zbl 1033.52009

[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. MR 1956842 | Zbl 1083.57024

[BO01] F. Bonahon and J.-P. Otal, Laminations mesurées de plissage des variétés hyperboliques de dimension 3. http://math.usc.edu/~fbonahon, 2001. Zbl 1083.57023

[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. Numdam | MR 1413855 | Zbl 0880.57005

[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. MR 1810534 | Zbl 0996.53029

[Brä92] W. Brägger, Kreispackungen und Triangulierungen. Enseign. Math. (2), 38(3-4):201-217, 1992. MR 1189006 | Zbl 0770.52007

[Cal61] E. Calabi, On compact Riemannian manifolds with constant curvature, I. AMS proceedings of Symposia in Pure Math, 3:155-180, 1961. MR 133787 | Zbl 0129.14102

[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. MR 1106755 | Zbl 0745.52010

[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. Zbl 0612.57010

[Fil] F. Fillastre, Surfaces convexes fuchsiennes. In preparation.

[Gro85] M. Gromov, Pseudo-holomorphic curves in symplectic manifolds. Inventiones Math., 82:307-347, 1985. Zbl 0592.53025

[Gro86] M. Gromov, Partial Differential Relations. Springer, 1986. MR 864505 | Zbl 0651.53001

[HK98] C.D. Hodgson and S.P. Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery. J. Differential Geom., 48:1-60, 1998. MR 1622600 | Zbl 0919.57009

[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. JFM 62.1217.04

[Lab89] F. Labourie, Immersions isométriques elliptiques et courbes pseudo-holomorphes. J. Differential Geom., 30:395-424, 1989. MR 1010166 | Zbl 0682.53063

[Lab92] F. Labourie, Métriques prescrites sur le bord des variétés hyperboliques de dimension 3. J. Differential Geom., 35:609-626, 1992. MR 1163450 | Zbl 0768.53017

[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. MR 1274933

[Lab97] F. Labourie, Problèmes de Monge-Ampère, courbes holomorphes et laminations. Geom. Funct. Anal., 7(3):496-534, 1997. MR 1466336 | Zbl 0885.32013

[Lab 00] F. Labourie, Un lemme de Morse pour les surfaces convexes. Invent. Math., 141 (2):239-297, 2000. MR 1775215 | Zbl 0981.52002

[LecO2] C. Lecuire, Plissage des variétés hyperboliques de dimension 3. Preprint 301, UMPA, ENS Lyon, 2002. MR 2207784

[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. MR 1752780 | Zbl 0968.53047

[Mes90] G. Mess, Lorentz spacetimes of constant curvature. Preprint I.H.E.S./M/90/28, 1990. MR 2328921

[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. MR 346714 | Zbl 0311.53067

[RH93] I. Rivin and C. D. Hodgson, A characterization of compact convex polyhedra in hyperbolic 3-space. Invent.Math., 111:77-111, 1993. MR 1193599 | Zbl 0784.52013

[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). MR 1280952 | Zbl 0823.52008

[Riv94] I. Rivin, Euclidean structures on simplicial surfaces and hyperbolic volume. Annals of Math., 139:553-580, 1994. MR 1283870 | Zbl 0823.52009

[Riv96] I. Rivin, A characterization of ideal polyhedra in hyperbolic 3-space. Annals of Math., 143:51-70, 1996. MR 1370757 | Zbl 0874.52006

[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. Numdam | MR 2075567 | Zbl 1061.52007

[Sch96] J.-M. Schlenker, Surfaces convexes dans des espaces lorentziens à courbure constante. Commun. Anal, and Geom., 4:285-331, 1996. MR 1393565 | Zbl 0864.53016

[Sch98a] J.-M. Schlenker, Métriques sur les polyèdres hyperboliques convexes. J. Differential Geom., 48 (2) :323-405, 1998. MR 1630178 | Zbl 0912.52008

[Sch98b] J.-M. Schlenker, Représentations de surfaces hyperboliques complètes dans H3. Annales de l'Institut Fourier, 48 (3):837-860, 1998. Numdam | MR 1644101 | Zbl 0916.53029

[Sch00] J.-M. Schlenker, Dihedral angles of convex polyhedra. Discrete Comput. Geom., 23 (3):409-417, 2000. MR 1744513 | Zbl 0951.52006

[Sch01a] textsc J.-M. Schlenker, Convex polyhedra in Lorentzian space-forms. Asian J. of Math., 5: 327-364, 2001. MR 1868937 | Zbl 1020.53046

[Sch01b] J.-M. Schlenker, Einstein manifolds with convex boundaries. Commentarii Math. Helvetici, 76(l) :l-28, 2001. MR 1819659 | Zbl 1036.53031

[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. MR 2208419

[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. Numdam | MR 556586 | Zbl 0439.30034

[Thu97] W.-P. Thurston, Three-dimensional geometry and topology. Recent version of the 1980 notes. http://wvwv.msri.org/publications/books/gt3m/, 1997. Zbl 0873.57001

[Tro91] M. Troyanov Prescribing curvature on compact surfaces with conical singularities. Trans. Amer. Math. Soc, 324(2):793-821, 1991. MR 1005085 | Zbl 0724.53023

[Wei60] A. Weil, On discrete subgroups of Lie groups. Annals of Math., 72(l):369-384, 1960. MR 137792 | Zbl 0131.26602

[Wei02] H. Weiss, Local rigidity of 3-dimensional cone-manifolds. PhD thesis, available at http://www.mathematik.uni-muenchen. de/personen/weiss.html, 2002.