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

页数：17

共 50 条

[1] Fully nonlinear equations on Riemannian manifolds with negative curvature
Gursky, MJ
Viaclovsky, JA
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2003, 52 (02) : 399 - 419
[2] ON ESTIMATES FOR FULLY NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS
Guan, Bo
Shi, Shujun
Sui, Zhenan
ANALYSIS & PDE, 2015, 8 (05): : 1145 - 1164
[3] The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds
Guan, Bo
ADVANCES IN MATHEMATICS, 2023, 415
[4] HOMOGENEOUS RIEMANNIAN MANIFOLDS OF NEGATIVE CURVATURE
KOBAYASHI, S
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1962, 68 (04) : 338 - &
[5] ON RIEMANNIAN MANIFOLDS OF CONSTANT NEGATIVE CURVATURE
Mirzaie, Reza
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2011, 48 (01) : 23 - 31
[6] The First Initial-Boundary Value Problem for a Class of Fully Nonlinear Parabolic Equations on Riemannian Manifolds
Jiao, Heming
Sui, Zhenan
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (09) : 2576 - 2595
[7] A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds
Alessandro Goffi
Francesco Pediconi
The Journal of Geometric Analysis, 2021, 31 : 8641 - 8665
[8] A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds
Goffi, Alessandro
Pediconi, Francesco
JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (08) : 8641 - 8665
[9] On a class of fully nonlinear elliptic equations on Hermitian manifolds
Bo Guan
Wei Sun
Calculus of Variations and Partial Differential Equations, 2015, 54 : 901 - 916
[10] On a class of fully nonlinear elliptic equations on Hermitian manifolds
Guan, Bo
Sun, Wei
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (01) : 901 - 916

← 1 2 3 4 5 →