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Geometric and Analytic Quasiconformality in Metric Measure Spaces

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Title: Geometric and Analytic Quasiconformality in Metric Measure Spaces
Author(s): Williams, Marshall
Abstract: 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).
Issue Date: 2012-04
Publisher: American Mathematical Society
Citation Info: Williams, M. (2012). "Geometric and Analytic Quasiconformality in Metric Measure Spaces." Proceedings of the American Mathematical Society 140(4): 1251-1266. DOI:10.1090/S0002-9939-2011-11035-9
Type: Article
Description: First published in Proceedings of the American Mathematical Society in volume 140 and issue 4, published by the American Mathematical Society
URI: http://hdl.handle.net/10027/8724
ISSN: 0002-9939
Sponsor: Partially supported under NSF awards 0602191, 0353549 and 0349290.
Date Available in INDIGO: 2012-10-02
 

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