The Dirichlet Problem for mixed Hessian type equations on Riemannian manifolds

2022/03/21 by xiaojuan Chen, Chen, Xiaojuan, Shi, Juhua +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2203.10755

openalex publication_date 2022/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive C² estimates for a class of mixed Hessian type equations with Dirichlet boundary condition, and obtain the existence theorem of admissible solutions for the classical Dirichlet problem of these mixed Hessian type equations.

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• The Dirichlet problem for a class of Hessian quotient equations on Riemannian manifolds
• The Neumann problem for a class of mixed complex Hessian equations