Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds

2021/12/06 by Huang, Liding, Zhang, Jiaogen · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.02919

Abstract

In this paper, we establish second order estimates for a general class of fully nonlinear equations with linear gradient terms on compact almost Hermitian manifolds. As an application, we first prove the existence of solutions for the Monge-Ampère equation with linear gradient terms for (n-1)-plurisubharmonic functions, originated from Gaudochon conjecture, in the almost Hermitian setting. Second, we solve the Monge-Ampère equation and Hessian equations with linear gradient terms. Third, we give the C^∞ a priori estimates for the deformed Hermitian-Yang-Mills equation with supercritical phase. At last, we prove the existence of deformed Hermitian-Yang-Mills equation and complex Hessian quotient equations under supersolutions.

Cited by

• A remark for fully non-linear elliptic equations on compact almost Hermitian manifolds
• The twisted constant in Calabi-Yau type equation

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