S0002-9939-2011-11035-9.pdf (265.6 kB)
Download file

Geometric and Analytic Quasiconformality in Metric Measure Spaces

Download (265.6 kB)
journal contribution
posted on 02.10.2012, 00:00 authored by Marshall Williams
We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism f : X → 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 f are related by KO(f) = esssupHO(x, f).

Funding

Partially supported under NSF awards 0602191, 0353549 and 0349290.

History

Publisher Statement

First published in Proceedings of the American Mathematical Society in volume 140 and issue 4, published by the American Mathematical Society

Publisher

American Mathematical Society

Language

en_US

issn

0002-9939

Issue date

01/04/2012

Usage metrics

Categories

Keywords

Exports