Yulun Xu (University of Toronto)

Title: Viscosity solution to complex Hessian quotient equation.

Abstract: We prove the existence of viscosity solutions to complex Hessian equations on compact Hermitian manifolds, assuming the existence of a strict subsolution in the viscosity sense. The results cover the complex Hessian quotient equations. This generalized our previous results where the equation needs to satisfy a determinant domination condition. This is a joint work with Prof. Jingrui Cheng.