On uniform estimate of complex elliptic equations on closed Hermitian manifolds

2014/12/16 by Wei Sun, Sun, Wei · 4 citations
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1412.5001

openalex publication_date 2014/12/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we study Hessian equations and complex quotient equations on closed Hermitian manifolds. We directly derive the uniform estimate for the admissible solution. As an application, we solve general Hessian equations on closed Kähler manifolds.

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• Parabolic Flow for Generalized complex Monge-Ampère type equations
• Generalized complex Monge-Ampère type equations on closed Hermitian manifolds
• A second order estimate for general complex Hessian equations
• A remark for fully non-linear elliptic equations on compact almost Hermitian manifolds

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