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Convex spacelike hypersurfaces of constant curvature in de Sitter space
1. | Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, United States |
References:
[1] |
L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge-Ampère equations,, Comm. Pure Applied Math., 37 (1984), 369.
doi: 10.1002/cpa.3160370306. |
[2] |
L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of eigenvalues of the Hessians,, Acta Math., 155 (1985), 261.
doi: 10.1007/BF02392544. |
[3] |
C. Gerhardt, "Curvature Problems,'', Series in Geometry and Topology, 39 (2006).
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B. Guan and J. Spruck, Hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity,, Amer. J. Math., 122 (2000), 1039.
doi: 10.1353/ajm.2000.0038. |
[5] |
B. Guan, J. Spruck and M. Szapiel, Hypersurfaces of constant curvature in hyperbolic space. I,, J. Geom. Anal., 19 (2009), 772.
doi: 10.1007/s12220-009-9086-7. |
[6] |
B. Guan and J. Spruck, Hypersurfaces of constant curvature in hyperbolic space. II,, J. European Math. Soc., 12 (2010), 797.
doi: 10.4171/JEMS/215. |
[7] |
B. Guan and J. Spruck, Convex hypersurfaces of constant curvature in Hyperbolic space,, in, (2011), 241. Google Scholar |
[8] |
S. W. Hawking and G. F. Ellis, "The Large Scale Structure of Spacetime,", Cambridge Monographs on Mathematical Physics, (1973).
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[9] |
S. Montiel, Complete non-compact spacelike hypersurfaces of constant mean curvature in de Sitter spaces,, J. Math. Soc. Japan, 55 (2003), 915.
doi: 10.2969/jmsj/1191418756. |
[10] |
B. Nelli and J. Spruck, On existence and uniqueness of constant mean curvature hypersurfaces in hyperbolic space,, in, (1996), 253.
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[11] |
V. Oliker, A priori estimates of the principal curvatures of spacelike hypersurfaces in de Sitter space with applications to hypersurfaces in hyperbolic space,, Amer. J. Math., 114 (1992), 605.
doi: 10.2307/2374771. |
[12] |
H. Rosenberg and J. Spruck, On the existence of convex hypersurfaces of constant Gauss curvature in hyperbolic space,, J. Differential Geom., 40 (1994), 379.
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[13] |
J.-M. Schlenker, Hypersurfaces in $H^n$ and the space of its horospheres,, Geom. Funct. Anal., 12 (2002), 395.
doi: 10.1007/s00039-002-8252-x. |
show all references
References:
[1] |
L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge-Ampère equations,, Comm. Pure Applied Math., 37 (1984), 369.
doi: 10.1002/cpa.3160370306. |
[2] |
L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of eigenvalues of the Hessians,, Acta Math., 155 (1985), 261.
doi: 10.1007/BF02392544. |
[3] |
C. Gerhardt, "Curvature Problems,'', Series in Geometry and Topology, 39 (2006).
|
[4] |
B. Guan and J. Spruck, Hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity,, Amer. J. Math., 122 (2000), 1039.
doi: 10.1353/ajm.2000.0038. |
[5] |
B. Guan, J. Spruck and M. Szapiel, Hypersurfaces of constant curvature in hyperbolic space. I,, J. Geom. Anal., 19 (2009), 772.
doi: 10.1007/s12220-009-9086-7. |
[6] |
B. Guan and J. Spruck, Hypersurfaces of constant curvature in hyperbolic space. II,, J. European Math. Soc., 12 (2010), 797.
doi: 10.4171/JEMS/215. |
[7] |
B. Guan and J. Spruck, Convex hypersurfaces of constant curvature in Hyperbolic space,, in, (2011), 241. Google Scholar |
[8] |
S. W. Hawking and G. F. Ellis, "The Large Scale Structure of Spacetime,", Cambridge Monographs on Mathematical Physics, (1973).
|
[9] |
S. Montiel, Complete non-compact spacelike hypersurfaces of constant mean curvature in de Sitter spaces,, J. Math. Soc. Japan, 55 (2003), 915.
doi: 10.2969/jmsj/1191418756. |
[10] |
B. Nelli and J. Spruck, On existence and uniqueness of constant mean curvature hypersurfaces in hyperbolic space,, in, (1996), 253.
|
[11] |
V. Oliker, A priori estimates of the principal curvatures of spacelike hypersurfaces in de Sitter space with applications to hypersurfaces in hyperbolic space,, Amer. J. Math., 114 (1992), 605.
doi: 10.2307/2374771. |
[12] |
H. Rosenberg and J. Spruck, On the existence of convex hypersurfaces of constant Gauss curvature in hyperbolic space,, J. Differential Geom., 40 (1994), 379.
|
[13] |
J.-M. Schlenker, Hypersurfaces in $H^n$ and the space of its horospheres,, Geom. Funct. Anal., 12 (2002), 395.
doi: 10.1007/s00039-002-8252-x. |
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