Quasiconformal, Lipschitz, and BV mappings in metric spaces

Abstract

Consider a mapping $f:X\to Y$ between two metric measure spaces. We study generalized versions of the local Lipschitz number $\mathrm{Lip}f$, as well as of the distortion number $H_f$ that is used to define quasiconformal mappings. Using these, we give sufficient conditions for $f$ being a BV mapping $f\in B{V}_{\mathrm{loc}}(X;Y)$ or a Newton-Sobolev mapping $f\in N_{\mathrm{loc}}^{1,p}(X;Y)$, with $1\le p<\infty$.