Description:

 Title: Regularization of Gamma-subharmonic Functions and Its Applications on Hessian Equations.

Abstract: We developed a method for regularizing Gamma-subharmonic functions, which generalize plurisubharmonic functions and are used in Hessian equations on Hermitian manifolds. Using this regularization method, we proved a H"older estimate for general Hessian equations on K"ahler manifolds with nonnegative holomorphic bisectional curvature, which generalizes the H"older estimate by Demailly, Guedj, Dinew, Hiep, Kolodziej, and Zeriahi for the complex Monge-Ampère equation. Additionally, we applied this regularization method to establish a uniqueness result for general Hessian equations on any Hermitian manifold, generalizing Lu's uniqueness result for σ_k equations on homogeneous Hermitian manifolds. This work is a collaboration with Jingrui Cheng.