Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds

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Abstract

We consider the properties of measurable maps of complete Riemannian manifolds which induce by composition isomorphisms of the Sobolev classes with generalized first variables whose exponent of integrability is distinct from the (Hausdorff) dimension of the manifold. We show that such maps can be re-defined on a null set so that they become quasi-isometries. Bibliography: 39 titles.

Original languageEnglish
Pages (from-to)59-104
Number of pages46
JournalSbornik Mathematics
Volume210
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • composition operator
  • quasi-isometric map
  • Riemannian manifold
  • Sobolev space
  • CARNOT GROUPS
  • SPACES
  • DIFFERENTIABILITY
  • ISOMORPHISMS
  • MAPPINGS
  • TRANSFORMATIONS

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