Subsolution theorem for the complex Hessian equation

TL;DR

This paper establishes a subsolution theorem for complex Hessian equations within smoothly bounded, strongly m-pseudoconvex domains in complex n-space, advancing the understanding of these equations in complex analysis.

Contribution

It proves the subsolution theorem for complex Hessian equations in specific pseudoconvex domains, a novel result in complex analysis.

Findings

Established the subsolution theorem for complex Hessian equations

Extended the theory to strongly m-pseudoconvex domains

Provided new tools for solving complex Hessian equations

Abstract

We prove the subsolution theorem for the complex Hessian equations in a smoothly bounded strongly $m$-pseudoconvex domain, $1 < m < n$, in $\bC^n$.