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This article is cited in 2 scientific papers (total in 2 papers)
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.
DOI:
https://doi.org/10.4213/sm8899
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English version:
Sbornik: Mathematics, 2019, 210:1, 59–104
Bibliographic databases:
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
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/msb8899https://doi.org/10.4213/sm8899 http://mi.mathnet.ru/eng/msb/v210/i1/p63
Citing articles on Google Scholar:
Russian citations,
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This publication is cited in the following articles:
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S. K. Vodopyanov, “Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings”, Siberian Math. J., 60:5 (2019), 774–804
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S. K. Vodopyanov, “O regulyarnosti otobrazhenii, obratnykh k sobolevskim, i teoriya $\mathscr{Q}_{q,p}$-gomeomorfizmov”, Sib. matem. zhurn., 61:6 (2020), 1257–1299
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