S0002-9939-2011-11035-9.pdf (265.6 kB)
Download fileGeometric and Analytic Quasiconformality in Metric Measure Spaces
journal contribution
posted on 2012-10-02, 00:00 authored by Marshall WilliamsWe 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).