Refined geometric characterizations of weak $p$-quasiconformal mappings

Abstract

In this paper we consider refined geometric characterizations of weak $p$-quasiconformal mappings $\phi :\Omega \to \tilde{\Omega }$, where $\Omega$ and $\tilde{\Omega }$ are domains in ${\mathbb{R}}^n$. We prove that mappings with the bounded on the set $\Omega \setminus S$, where a set $S$ has $\sigma$-finite $(n-1)$-measure, geometric $p$-dilatation, are $W^1_{p,\loc}$-- mappings and generate bounded composition operators on Sobolev spaces.

12 pages. arXiv admin note: text overlap with arXiv:2312.10182