Hypersurfaces of constant curvature in hyperbolic space II

被引：17

作者：

Guan, Bo ^{[1
]}

Spruck, Joel ^{[2
]}

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[2] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2010年 / 12卷 / 03期

基金：

美国国家科学基金会;

关键词：

Hyperbolic space; hypersurfaces of constant curvature; asymptotic boundary; fully nonlinear elliptic equations; 2ND-ORDER ELLIPTIC-EQUATIONS; CONVEX HYPERSURFACES; DIRICHLET PROBLEM; BOUNDARY;

D O I：

10.4171/JEMS/215

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This is the second of a series of papers in which we investigate the problem of finding, in hyperbolic space, complete hypersurfaces of constant curvature with a prescribed asymptotic boundary at infinity for a general class of curvature functions. In this paper we focus on graphs over a domain with nonnegative mean curvature.

引用

页码：797 / 817

页数：21

共 50 条

[21] Quantitative Stability for Hypersurfaces with Almost Constant Mean Curvature in the Hyperbolic Space
Ciraolo, Giulio
Vezzoni, Luigi
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2020, 69 (04) : 1105 - 1153
[22] Hypersurfaces of a space of constant curvature
Fialkow, A
[J]. ANNALS OF MATHEMATICS, 1938, 39 : 762 - 785
[23] HYPERSURFACES OF CONSTANT SCALAR CURVATURE IN HYPERBOLIC SPACE WITH PRESCRIBED ASYMPTOTIC BOUNDARY AT INFINITY
Wang, Bin
[J]. arXiv,
[24] SOME REMARKS ON EMBEDDED HYPERSURFACES IN HYPERBOLIC SPACE OF CONSTANT CURVATURE AND SPHERICAL BOUNDARY
NELLI, B
ROSENBERG, H
[J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 1995, 13 (01) : 23 - 30
[25] Hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity
Guan, B
Spruck, J
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2000, 122 (05) : 1039 - 1060
[26] Curvature flow of complete hypersurfaces in hyperbolic space
Xiao, Ling
[J]. GEOMETRIAE DEDICATA, 2013, 164 (01) : 357 - 383
[27] Curvature flow of complete hypersurfaces in hyperbolic space
Ling Xiao
[J]. Geometriae Dedicata, 2013, 164 : 357 - 383
[28] ON 2 CLASSES OF HYPERSURFACES IN A SPACE OF CONSTANT CURVATURE
WU, CX
[J]. LECTURE NOTES IN MATHEMATICS, 1987, 1255 : 160 - 172
[29] Hypersurfaces with Constant Mean Curvature in Space Forms
Song Hongzao
Hu Zejun
Hu Conge(Henan University) (Zhengzhou University) (Henan University)
[J]. Chinese Quarterly Journal of Mathematics, 1996, (01) : 42 - 48
[30] HYPERSURFACES OF MINKOWSKI SPACE WITH CONSTANT MEAN CURVATURE
Li, Jintang
[J]. HOUSTON JOURNAL OF MATHEMATICS, 2013, 39 (01): : 137 - 145

← 1 2 3 4 5 →