Mappings of finite distortion between metric measure spaces

Guo, Chang-yu

doi:10.1090/ecgd/277

Mappings of finite distortion between metric measure spaces
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by Chang-yu Guo PDF

Conform. Geom. Dyn. 19 (2015), 95-121 Request permission

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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