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Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. / Vodopyanov, S. K.

In: Sbornik Mathematics, Vol. 210, No. 1, 01.01.2019, p. 59-104.

Research output: Contribution to journal › Article › peer-review

Harvard

Vodopyanov, SK 2019, 'Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds', Sbornik Mathematics, vol. 210, no. 1, pp. 59-104. https://doi.org/10.1070/SM8899

APA

Vodopyanov, S. K. (2019). Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. Sbornik Mathematics, 210(1), 59-104. https://doi.org/10.1070/SM8899

Vancouver

Vodopyanov SK. Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. Sbornik Mathematics. 2019 Jan 1;210(1):59-104. doi: 10.1070/SM8899

Author

Vodopyanov, S. K. / Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. In: Sbornik Mathematics. 2019 ; Vol. 210, No. 1. pp. 59-104.

BibTeX

@article{dd53bd2531b4494aab8ee1b64c915b36,
title = "Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds",
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 = "composition operator, quasi-isometric map, Riemannian manifold, Sobolev space, CARNOT GROUPS, SPACES, DIFFERENTIABILITY, ISOMORPHISMS, MAPPINGS, TRANSFORMATIONS",
author = "Vodopyanov, {S. K.}",
year = "2019",
month = jan,
day = "1",
doi = "10.1070/SM8899",
language = "English",
volume = "210",
pages = "59--104",
journal = "Sbornik Mathematics",
issn = "1064-5616",
publisher = "Turpion Ltd.",
number = "1",

}

RIS

TY - JOUR

T1 - Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds

AU - Vodopyanov, S. K.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - composition operator

KW - quasi-isometric map

KW - Riemannian manifold

KW - Sobolev space

KW - CARNOT GROUPS

KW - SPACES

KW - DIFFERENTIABILITY

KW - ISOMORPHISMS

KW - MAPPINGS

KW - TRANSFORMATIONS

UR - http://www.scopus.com/inward/record.url?scp=85067941987&partnerID=8YFLogxK

U2 - 10.1070/SM8899

DO - 10.1070/SM8899

M3 - Article

AN - SCOPUS:85067941987

VL - 210

SP - 59

EP - 104

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 1

ER -

ID: 20711345