Viscosity solution to complex Hessian quotient equations

TL;DR

This paper establishes the existence of viscosity solutions for complex Hessian quotient equations on compact Hermitian manifolds, broadening previous results by removing the determinant domination condition.

Contribution

It proves the existence of viscosity solutions to complex Hessian quotient equations assuming a strict subsolution, extending prior work to more general equations.

Findings

Existence of viscosity solutions on compact Hermitian manifolds

Extension to complex Hessian quotient equations

Removal of the determinant domination condition

Abstract

In this paper, 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.