Des immersions isométriques de surfaces aux variétés hyperboliques à bord convexe
Séminaire de théorie spectrale et géométrie, Tome 21 (2002-2003), pp. 165-216. 
@article{TSG_2002-2003__21__165_0,
     author = {Schlenker, Jean-Marc},
     title = {Des immersions isom\'etriques de surfaces aux vari\'et\'es hyperboliques \`a bord convexe},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {165--216},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {21},
     year = {2002-2003},
     mrnumber = {2052831},
     zbl = {1059.53055},
     language = {fr},
     url = {http://www.numdam.org/item/TSG_2002-2003__21__165_0/}
}
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
SP  - 165
EP  - 216
VL  - 21
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/item/TSG_2002-2003__21__165_0/
LA  - fr
ID  - TSG_2002-2003__21__165_0
ER  - 
%0 Journal Article
%A Schlenker, Jean-Marc
%T Des immersions isométriques de surfaces aux variétés hyperboliques à bord convexe
%J Séminaire de théorie spectrale et géométrie
%D 2002-2003
%P 165-216
%V 21
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/item/TSG_2002-2003__21__165_0/
%G fr
%F TSG_2002-2003__21__165_0
Schlenker, Jean-Marc. Des immersions isométriques de surfaces aux variétés hyperboliques à bord convexe. Séminaire de théorie spectrale et géométrie, Tome 21 (2002-2003), pp. 165-216. http://www.numdam.org/item/TSG_2002-2003__21__165_0/

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

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

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

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

[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

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

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

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

[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 | Zbl

[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

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

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

[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

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

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

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

[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 | Zbl

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

[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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

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

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

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

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

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

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

[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

[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 | Zbl

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

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

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

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