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Mappings of finite distortion between metric measure spaces


Author: Chang-yu Guo
Journal: Conform. Geom. Dyn. 19 (2015), 95-121
MSC (2010): Primary 30C65; Secondary 30L99, 57P99
DOI: https://doi.org/10.1090/ecgd/277
Published electronically: April 24, 2015
MathSciNet review: 3338960
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Abstract: We establish the basic analytic properties of mappings of finite distortion between proper Ahlfors regular metric measure spaces that support a $ (1,1)$-Poincaré inequality. As applications, we prove that under certain integrability assumption for the distortion function, the branch set of a mapping of finite distortion between generalized $ n$-manifolds of type $ A$ has zero Hausdorff $ n$-measure.


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Additional Information

Chang-yu Guo
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FI-40014 University of Jyväskylä, Finland
Email: changyu.c.guo@jyu.fi

DOI: https://doi.org/10.1090/ecgd/277
Received by editor(s): October 24, 2014
Published electronically: April 24, 2015
Additional Notes: The author was partially supported by the Academy of Finland grant 131477 and the Magnus Ehrnrooth foundation.
Article copyright: © Copyright 2015 American Mathematical Society

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