Surfaces à courbure extrinsèque négative dans l'espace hyperbolique
Schlenker, Jean-Marc
Annales scientifiques de l'École Normale Supérieure, Tome 34 (2001), p. 79-130 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_2001_4_34_1_79_0,
     author = {Schlenker, Jean-Marc},
     title = {Surfaces \`a courbure extrins\`eque n\'egative dans l'espace hyperbolique},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {34},
     year = {2001},
     pages = {79-130},
     doi = {10.1016/s0012-9593(00)01057-0},
     mrnumber = {1833091},
     zbl = {1029.53068},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_2001_4_34_1_79_0}
}

Schlenker, Jean-Marc. Surfaces à courbure extrinsèque négative dans l'espace hyperbolique. Annales scientifiques de l'École Normale Supérieure, Tome 34 (2001) pp. 79-130. doi : 10.1016/s0012-9593(00)01057-0. http://gdmltest.u-ga.fr/item/ASENS_2001_4_34_1_79_0/

[1] Burago Yu.D, Shefel' S.Z, The geometry of surfaces in Euclidean spaces, in: Burago Yu.D, Zalgaller V.A (Eds.), Geometry III, Chapter I, Springer-Verlag, 1992, pp. 1-86, (Encyclopaedia of Mathematical Sciences, Vol. 48). | MR 1306734 | Zbl 0781.53006

[2] Efimov N.V, Apparition of singularities on surfaces with negative curvature, Mat. Sbornik 64 ((106) 2) (1964) 286-320. | MR 167938 | Zbl 0126.37402

[3] Efimov N.V, Surfaces with a slowly changing negative curvature, Russian Math. Surveys 5 (131) (1966) 1-56. | MR 202092 | Zbl 0171.19903

[4] Efimov N.V, Hyperbolic problems in the theory of surfaces, in: Proc. Internat. Congr. Math. (Moscow, 1966), Mir, Moscow, 1968, pp. 177-188. | MR 238232 | Zbl 0188.53604

[5] Gallot S, Hulin D, Lafontaine J, Riemannian Geometry, Springer-Verlag, 1987. | MR 909697 | Zbl 0636.53001

[6] Hilbert D, Über Fläschen von konstanter Gaußscher Krummung, Trans. Amer. Math. Soc. 2 (1901) 87-99. | JFM 32.0608.01

[7] Hong J.X, Realization in R3 of complete Riemannian manifolds with negative curvature, Comm. Anal. Geom. 1 (3-4) (1993) 487-514. | Zbl 0856.53004

[8] Klotz-Milnor T, Efimov's theorem about complete immersed surfaces of negative curvature, Adv. in Math. 8 (1972) 474-543. | MR 301679 | Zbl 0236.53055

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

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

[11] Poznjak È.G, Regular realization in the large of two-dimensional metrics of negative curvature, Dokl. Akad. Nauk SSSR 170 (1966) 786-789. | MR 205204 | Zbl 0168.19501

[12] Poznyak È.G, Shikin E.V, Small parameters in the theory of isometric imbeddings of two-dimensional Riemannian manifolds in Euclidean spaces, in: Some Questions of Differential Geometry in the Large, Amer. Math. Soc, Providence, RI, 1996, pp. 151-192. | MR 1406844 | Zbl 0862.53004

[13] Rozendorn E.R, An isolated point on a surface of negative curvature with a regular metric, Soviet Math. 3 (1962) 473-477. | Zbl 0123.15502

[14] Rozendorn E.R, Surfaces of negative curvature, in: Burago Yu.D, Zalgaller V.A (Eds.), Geometry III, Chapter II, Springer-Verlag, 1992, pp. 87-178, (Encyclopaedia of Mathematical Sciences, Vol. 48). | MR 1306735 | Zbl 0781.53007

[15] Schlenker J.-M, Surfaces convexes dans des espaces lorentziens à courbure constante, Comm. Anal. Geom. 4 (1996) 285-331. | MR 1393565 | Zbl 0864.53016

[16] Schlenker J.-M, Complete surfaces with negative extrinsic curvature, Preprint, 1999, http://xxx.lanl.gov/abs/math.DG/9912101.

[17] Shikin E.V, The global isometric immersion in R3 of certain metrics of nonpositive curvature, Dokl. Akad. Nauk SSSR 215 (1974) 61-63. | MR 343218 | Zbl 0299.53038

[18] Smyth B, Efimov's inequality and other inequalities in a sphere, in: Geometry and Topology of Submanifolds, IV (Leuven, 1991), World Sci. Publishing, River Edge, NJ, 1992, pp. 76-86. | MR 1185718 | Zbl 0839.53038

[19] Spivak M, A Comprehensive Introduction to Geometry, Vols. I-V, Publish or perish, 1970-1975. | MR 394453 | Zbl 0306.53003

[20] Smyth B, Xavier F, Efimov's theorem in dimension greater than two, Invent. Math. 90 (1987) 443-450. | MR 914845 | Zbl 0642.53007

[21] Tunitskiĭ D.V, Global regular isometric embedding of two-dimensional metrics with nonpositive curvature, Mat. Sbornik 183 (7) (1992) 65-80. | MR 1186975 | Zbl 0773.53001