A class of fully nonlinear equations on Riemannian manifolds with negative curvature

被引：0
作者：
Chen, Li [1 ]
He, Yan [1 ]
机构：
[1] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2024年 / 63卷 / 06期
关键词：
Primary; 35J96; 52A39; Secondary; 53A05; BOUNDARY-VALUE-PROBLEMS; 2ND-ORDER ELLIPTIC-EQUATIONS; COMPLETE CONFORMAL METRICS; MONGE-AMPERE-TYPE; YAMABE PROBLEM; DIRICHLET PROBLEM; RICCI CURVATURE; EXISTENCE; FLOW; EIGENVALUES;
D O I：
10.1007/s00526-024-02756-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a class of fully nonlinear equations on Riemannian manifolds with negative curvature which naturally arise in conformal geometry. Moreover, we prove the a priori estimates for solutions to these equations and establish the existence results. Our results can be viewed as an extension of previous results given by Gursky-Viaclovsky and Li-Sheng.
引用
收藏
页数：17
相关论文
共 62 条
[1]  
AUBIN T, 1976, J MATH PURE APPL, V55, P269
[2]  
Brendle S, 2004, CALC VAR PARTIAL DIF, V20, P399, DOI 10.1007/s00526-003-0234-9
[3]  
Brendle S, 2009, J DIFFER GEOM, V81, P225, DOI 10.4310/jdg/1231856261
[4]   THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .1. MONGE-AMPERE EQUATION [J].
CAFFARELLI, L ;
NIRENBERG, L ;
SPRUCK, J .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1984, 37 (03) :369-402
[5]   THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .3. FUNCTIONS OF THE EIGENVALUES OF THE HESSIAN [J].
CAFFARELLI, L ;
NIRENBERG, L ;
SPRUCK, J .
ACTA MATHEMATICA, 1985, 155 (3-4) :261-301
[6]   An a priori estimate for a fully nonlinear equation on four-manifolds [J].
Chang, SYA ;
Gursky, MJ ;
Yang, P .
JOURNAL D ANALYSE MATHEMATIQUE, 2002, 87 (1) :151-186
[7]   An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature [J].
Chang, SYA ;
Gursky, MJ ;
Yang, PC .
ANNALS OF MATHEMATICS, 2002, 155 (03) :709-787
[8]   A Class of Fully Nonlinear Equations Arising in Conformal Geometry [J].
Chen, Li ;
Guo, Xi ;
He, Yan .
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (05) :3651-3676
[9]  
Chen SYS, 2005, INT MATH RES NOTICES, V2005, P3403
[10]   Boundary value problems for some fully nonlinear elliptic equations [J].
Chen, Szu-yu Sophie .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2007, 30 (01) :1-15
1234567