Affordable Access

Geometric and analytic quasiconformality in metric measure spaces

Authors
Type
Preprint
Publication Date
Submission Date
Source
arXiv
License
Yellow
External links

Abstract

We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism $f\colon X\rightarrow Y$ between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either space. When $X$ and $Y$ have locally $Q$-bounded geometry and $Y$ is contained in an Alexandrov space of curvature bounded above, the sharpness of our results implies that, as in the classical case, the modular and pointwise outer dilatations of $\map$ are related by $K_O(f)= \operatorname{esssup} H_O(x,f)$.

Statistics

Seen <100 times