-
Previous Article
Spreading speeds and traveling waves for non-cooperative integro-difference systems
- DCDS-B Home
- This Issue
-
Next Article
Lyapunov-Schmidt reduction for optimal control problems
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).
|
[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. |
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. |
[1] |
Makoto Nakamura. Remarks on a dispersive equation in de Sitter spacetime. Conference Publications, 2015, 2015 (special) : 901-905. doi: 10.3934/proc.2015.0901 |
[2] |
Yannan Liu, Hongjie Ju. Non-collapsing for a fully nonlinear inverse curvature flow. Communications on Pure & Applied Analysis, 2017, 16 (3) : 945-952. doi: 10.3934/cpaa.2017045 |
[3] |
Karen Yagdjian. The semilinear Klein-Gordon equation in de Sitter spacetime. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 679-696. doi: 10.3934/dcdss.2009.2.679 |
[4] |
Elias M. Guio, Ricardo Sa Earp. Existence and non-existence for a mean curvature equation in hyperbolic space. Communications on Pure & Applied Analysis, 2005, 4 (3) : 549-568. doi: 10.3934/cpaa.2005.4.549 |
[5] |
Qinian Jin, YanYan Li. Starshaped compact hypersurfaces with prescribed $k$-th mean curvature in hyperbolic space. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 367-377. doi: 10.3934/dcds.2006.15.367 |
[6] |
Ali Hyder, Luca Martinazzi. Conformal metrics on $\mathbb{R}^{2m}$ with constant Q-curvature, prescribed volume and asymptotic behavior. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 283-299. doi: 10.3934/dcds.2015.35.283 |
[7] |
Limei Dai. Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1707-1714. doi: 10.3934/cpaa.2011.10.1707 |
[8] |
Fabio Punzo. Support properties of solutions to nonlinear parabolic equations with variable density in the hyperbolic space. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 657-670. doi: 10.3934/dcdss.2012.5.657 |
[9] |
Misha Bialy. On Totally integrable magnetic billiards on constant curvature surface. Electronic Research Announcements, 2012, 19: 112-119. doi: 10.3934/era.2012.19.112 |
[10] |
Matthias Eller. Loss of derivatives for hyperbolic boundary problems with constant coefficients. Discrete & Continuous Dynamical Systems - B, 2018, 23 (3) : 1347-1361. doi: 10.3934/dcdsb.2018154 |
[11] |
Doan The Hieu, Tran Le Nam. The classification of constant weighted curvature curves in the plane with a log-linear density. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1641-1652. doi: 10.3934/cpaa.2014.13.1641 |
[12] |
Jérôme Bertrand. Prescription of Gauss curvature on compact hyperbolic orbifolds. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1269-1284. doi: 10.3934/dcds.2014.34.1269 |
[13] |
Qianzhong Ou. Nonexistence results for a fully nonlinear evolution inequality. Electronic Research Announcements, 2016, 23: 19-24. doi: 10.3934/era.2016.23.003 |
[14] |
Isabeau Birindelli, Stefania Patrizi. A Neumann eigenvalue problem for fully nonlinear operators. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 845-863. doi: 10.3934/dcds.2010.28.845 |
[15] |
Isabeau Birindelli, Francoise Demengel. The dirichlet problem for singluar fully nonlinear operators. Conference Publications, 2007, 2007 (Special) : 110-121. doi: 10.3934/proc.2007.2007.110 |
[16] |
Luis Caffarelli, Luis Duque, Hernán Vivas. The two membranes problem for fully nonlinear operators. Discrete & Continuous Dynamical Systems - A, 2018, 38 (12) : 6015-6027. doi: 10.3934/dcds.2018152 |
[17] |
Meng Qu, Ping Li, Liu Yang. Symmetry and monotonicity of solutions for the fully nonlinear nonlocal equation. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1337-1349. doi: 10.3934/cpaa.2020065 |
[18] |
Gábor Székelyhidi, Ben Weinkove. On a constant rank theorem for nonlinear elliptic PDEs. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6523-6532. doi: 10.3934/dcds.2016081 |
[19] |
Julián Fernández Bonder, Julio D. Rossi. Asymptotic behavior of the best Sobolev trace constant in expanding and contracting domains. Communications on Pure & Applied Analysis, 2002, 1 (3) : 359-378. doi: 10.3934/cpaa.2002.1.359 |
[20] |
David L. Finn. Noncompact manifolds with constant negative scalar curvature and singular solutions to semihnear elliptic equations. Conference Publications, 1998, 1998 (Special) : 262-275. doi: 10.3934/proc.1998.1998.262 |
2018 Impact Factor: 1.008
Tools
Metrics
Other articles
by authors
[Back to Top]