The Dirichlet problem for a class of Hessian quotient equations on Riemannian manifolds

2021/05/19 by Xiaojuan Chen, Qiang Tu, Chen, Xiaojuan +3 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Primary 35J15 #Secondary 35B45

paper · pdf · doi:10.48550/arxiv.2105.09069

openalex publication_date 2021/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the Dirichlet problem for a class of Hessian quotient equations on Riemannian manifolds. Under the assumption of an admissible subsolution, we solve the existence and the uniquness for the Dirichlet problem in a domain without any geometric restrictions on the boundary, based on the a priori estimates for the solutions to the Hessian quotient type equations.

Citations

• Convexity estimates for mean curvature flow and singularities of mean convex surfaces
• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian

Cited by

• Asymptotic Plateau problem for 2-convex hypersurface in ℍ⁴
• The Dirichlet problem for Hessian quotient type curvature equations in Minkowski space

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