Mappings with bounded (P,Q)-distortion on Carnot groups

A. Ukhlov, S. K. Vodop'yanov

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We study mappings with bounded (p,q)-distortion associated to Sobolev spaces on Carnot groups. Mappings of such type have applications to the Sobolev type embedding theory and classification of manifolds. For this class of mappings, we obtain estimates of linear distortion, and a geometrical description. We prove also Liouville type theorems and give some sufficient conditions for removability of sets.

Original languageEnglish
Pages (from-to)605-634
Number of pages30
JournalBulletin des Sciences Mathematiques
Volume134
Issue number6
DOIs
StatePublished - 1 Sep 2010

Keywords

  • Carnot groups
  • Mappings with bounded distortion
  • Sobolev spaces

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