On a family of quasimetric spaces in generalized potential theory

TL;DR

This paper introduces a new family of quasimetric spaces in generalized potential theory that include m-subharmonic functions with finite energy, improving stability results for complex Hessian equations.

Contribution

It constructs and analyzes a novel family of quasimetric spaces in generalized potential theory, applicable in complex analysis and Kähler geometry, enhancing stability results for complex Hessian equations.

Findings

Defined a new family of quasimetric spaces in potential theory

Applied these spaces to improve stability results for complex Hessian equations

Extended the framework to both  ext{C}^n and compact Ke4hler manifolds

Abstract

We construct a family of quasimetric spaces in generalized potential theory containing $m$-subharmonic functions with finite $(p,m)$-energy. These quasimetric spaces will be viewed both in $\mathbb{C}^n$ and in compact K\"ahler manifolds, and their convergence will be used to improve known stability results for the complex Hessian equations.