The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds
报告题目(Title)：The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds
报告人(Speaker)：郑涛 博士 （北京理工大学）
地点(Place)：后主楼1223
时间(Time)：2019年10月22日 14:30-15:30
邀请人(Inviter)：汪志威
报告摘要
We study the Dirichlet problem of a class of fully nonlinear elliptic equations on Hermitian manifolds and derive a priori $C^2$ estimates which depend on the initial data on manifolds, the admissible subsolutions and the upper bound of the gradients of the solutions. In some special cases, we also obtain the gradient estimates, and hence we can solve the corresponding Dirichlet problem with admissible subsolutions, which is mainly motivated by our alternative proof of the upper bound of the gradients of the solutions to the equations related to the $(m-1)$-plurisubharmonic functions solved by Tosatti \& Weinkove and to the Gauduchon conjecture solved by Sz\'ekelyhidi, Tosatti \& Weinkove on the compact Hermitian manifolds without boundary.This is a joint work with Dr. Ke Feng and Professor Huabin Ge.
