A class of prescribed shifted curvature problems on the horo-convex hypersurfaces in Hn+1

被引：0

作者：

Ji, Zhengchao ^{[1
,2
]}

机构：

[1] China Jiliang Univ, Dept Math, Hangzhou 310018, Peoples R China

[2] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2025年 / 541卷 / 02期

关键词：

Hyperbolic spaces; Shifted principal curvature; Horo-convex; CLOSED WEINGARTEN HYPERSURFACES; SHAPED COMPACT HYPERSURFACES; EQUATIONS;

D O I：

10.1016/j.jmaa.2024.128720

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the prescribed shifted curvature problems on horo-convex hypersurfaces in Hn+1. By establishing the C-0, C-1 and C-2 estimates to the solutions of these problems, we obtain some existence theorems to several Monge-Amp & egrave;re type equations. Our results will give solutions to a general class of prescribed shifted curvature problems. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：21

共 25 条

[1] CONTRACTION OF CONVEX HYPERSURFACES IN EUCLIDEAN-SPACE
ANDREWS, B
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1994, 2 (02) : 151 - 171
[2] Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space
Andrews, Ben
Chen, Xuzhong
Wei, Yong
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2021, 23 (07) : 2467 - 2509
[3] DIFFERENTIABILITY PROPERTIES OF SYMMETRIC AND ISOTROPIC FUNCTIONS
BALL, JM
[J]. DUKE MATHEMATICAL JOURNAL, 1984, 51 (03) : 699 - 728
[4] THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .3. FUNCTIONS OF THE EIGENVALUES OF THE HESSIAN
CAFFARELLI, L
NIRENBERG, L
SPRUCK, J
[J]. ACTA MATHEMATICA, 1985, 155 (3-4) : 261 - 301
[5] Starshaped compact hypersurfaces with prescribed Weingarten curvature in warped product manifolds
Chen, Daguang
Li, Haizhong
Wang, Zhizhang
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2018, 57 (02)
[6] Chen L, 2021, J GEOM ANAL, V31, P6349, DOI 10.1007/s12220-020-00533-9
[7] Christoffel E. B., 1865, J REINE ANGEW MATH, V64, P193
[8] Closed Weingarten Hypersurfaces in Warped Product Manifolds
de Andrade, Francisco J.
Barbosa, Joao Lucas M.
de Lira, Jorge H. S.
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2009, 58 (04) : 1691 - 1718
[9] Espinar JM, 2009, J EUR MATH SOC, V11, P903
[10] Evans L.C., 1996, J. Differ. Geom., V43, P612

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