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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 5, Pages 996–1034
DOI: https://doi.org/10.33048/smzh.2019.60.503 (Mi smj3130) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings

S. K. Vodopyanovab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (737 kB) Citations (6)
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DOI: https://doi.org/10.33048/smzh.2019.60.503
Abstract: We prove that a measurable mapping of domains in a complete Riemannian manifold induces an isomorphism of Sobolev spaces with the first generalized derivatives whose summability exponent equals the (Hausdorff) dimension of the manifold if and only if the mapping coincides with some quasiconformal mapping almost everywhere.
Keywords: Riemannian manifold, quasiconformal mapping, Sobolev space, composition operator.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.a03.21.0008
Russian Foundation for Basic Research 17-01-00801_а
The author was supported by the Ministry of Education and Science (Contract No. 02.a03.21.0008) and the Russian Foundation for Basic Research (Grant 17-01-00801).
Received: 27.03.2019
Revised: 27.03.2019
Accepted: 15.05.2019
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 5, Pages 774–804
DOI: https://doi.org/10.1134/S0037446619050033
Bibliographic databases:
Document Type: Article
UDC: 517.518+517.54
Language: Russian
Citation: S. K. Vodopyanov, “Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings”, Sibirsk. Mat. Zh., 60:5 (2019), 996–1034; Siberian Math. J., 60:5 (2019), 774–804
Citation in format AMSBIB
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\paper Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings
\jour Sibirsk. Mat. Zh.
\yr 2019
\vol 60
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\pages 996--1034
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\transl
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  • https://www.mathnet.ru/eng/smj3130
  • https://www.mathnet.ru/eng/smj/v60/i5/p996
    • This publication is cited in the following 6 articles:
    1. S. K. Vodopyanov, “Composition operators in Sobolev spaces on Riemannian manifolds”, Siberian Math. J., 65:6 (2024), 1305–1326  mathnet  crossref  crossref
    2. S. K. Vodopyanov, “Coincidence of set functions in quasiconformal analysis”, Sb. Math., 213:9 (2022), 1157–1186  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. S. K. Vodopyanov, N. A. Evseev, “Functional and analytical properties of a class of mappings of quasiconformal analysis on Carnot groups”, Siberian Math. J., 63:2 (2022), 233–261  mathnet  crossref  crossref
    4. S. K. Vodopyanov, “TWO-WEIGHTED COMPOSITION OPERATORS ON SOBOLEV SPACES AND QUASICONFORMAL ANALYSIS”, J Math Sci, 266:3 (2022), 491  crossref
    5. S. K. Vodopyanov, “On the equivalence of two approaches to problems of quasiconformal analysis”, Siberian Math. J., 62:6 (2021), 1010–1025  mathnet  crossref  crossref  isi  elib
    6. S. K. Vodopyanov, “The regularity of inverses to Sobolev mappings and the theory of Qq,p-homeomorphisms”, Siberian Math. J., 61:6 (2020), 1002–1038  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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