On admissible changes of variables for Sobolev functions on (sub)Riemannian manifolds

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• 作者：S. K. Vodopyanov
• 刊名：Doklady Mathematics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：93
• 期：3
• 页码：318-321
• 全文大小：272 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1531-8362
• 卷排序：93

文摘

We give a description of metric properties of measurable mappings of domains on Riemannian manifolds inducing isomorphisms of Sobolev spaces by the composition rule. We prove that any such mapping can be redefined on a set of measure zero to be quasi-isometric, when the exponent of summability is different from the dimension of a Riemannian manifold or to coincide with a quasi-conformal mapping otherwise.The article was translated by the author.Original Russian Text © S.K. Vodopyanov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 468, No. 6, pp. 609–613.Presented by Academician of the RAS Yu.G. Reshetnyak February 1, 2016