Fully non-linear elliptic equations on compact almost Hermitian manifolds
题目: Fully non-linear elliptic equations on compact almost Hermitian manifolds
摘要: We will talk about a priori estimates for solutions of a general class of fully non-linear equations on compact almost Hermitian manifolds. As an application, we will solve the complex Hessian equation and the Monge--Ampère equation for (n-1)-plurisubharmonic equations in the almost Hermitian setting. We will also show the second order estimates for the fully nonlinear elliptic equations with gradient terms, including the deformed Hermitian-Yang-Mills equation and the equation in the proof of Gauduchon conjecture by Szekelyhidi-Tosatti-Weinkove.