Geometric and Analytic Quasiconformality in Metric Measure Spaces
journal contributionposted on 2012-10-02, 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).
Partially supported under NSF awards 0602191, 0353549 and 0349290.
Publisher StatementFirst published in Proceedings of the American Mathematical Society in volume 140 and issue 4, published by the American Mathematical Society
PublisherAmerican Mathematical Society