On a family of quasimetric spaces in generalized potential theory

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 Kähler manifolds, and their convergence will be used to improve known stability results for the complex Hessian equations.