Isomorphisms of Sobolev Spaces on Riemannian Manifolds and Quasiconformal Mappings

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Abstract

We prove that a measurable mapping of domains in a complete Riemannian manifold induces an isomorphism of Sobolev spaces with the first generalized derivatives whose summability exponent equals the (Hausdorff) dimension of the manifold if and only if the mapping coincides with some quasiconformal mapping almost everywhere.

Original languageEnglish
Pages (from-to)774-804
Number of pages31
JournalSiberian Mathematical Journal
Volume60
Issue number5
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

  • composition operator
  • quasiconformal mapping
  • Riemannian manifold
  • Sobolev space

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