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Mat. Sb., 2019, Volume 210, Number 1, Pages 63–112 (Mi msb8899)  
Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds

S. K. Vodopyanovab

a Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Faculty of Mechanics and Mathematics of Novosibirsk National Research State University, Novosibirsk, Russia

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.

Keywords: Riemannian manifold, quasi-isometric map, Sobolev space, composition operator.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.3087.2017/4.6
Russian Foundation for Basic Research 17-01-00801-а
The results in § 5.2 were obtained within the framework of a state assignment of the Ministry of Education and Science of the Russian Federation (grant no. 1.3087.2017/4.6) and the results in § 5.1 we obtained with the support of the Russian Foundation for Basic Research (grant no. 17-01-00801-a).


DOI: https://doi.org/10.4213/sm8899

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English version:
Sbornik: Mathematics, 2019, 210:1, 59–104

Bibliographic databases:

Document Type: Article
UDC: 517.518+517.54
MSC: Primary 46E35, 58C25; Secondary 30C65
Received: 29.12.2016 and 19.07.2018

Citation: S. K. Vodopyanov, “Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds”, Mat. Sb., 210:1 (2019), 63–112; Sb. Math., 210:1 (2019), 59–104

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