Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2019, Volume: 60, Number: 5, Pages: 774-804 Pages count : 29 DOI: 10.1134/S0037446619050033 | ||||
| Tags | Riemannian manifold, quasiconformal mapping, Sobolev space, composition operator | ||||
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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.
Cite:
Vodopʹyanov S.K.
Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings
Siberian Mathematical Journal. 2019. V.60. N5. P.774-804. DOI: 10.1134/S0037446619050033 WOS Scopus OpenAlex
Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings
Siberian Mathematical Journal. 2019. V.60. N5. P.774-804. DOI: 10.1134/S0037446619050033 WOS Scopus OpenAlex
Original:
Водопьянов С.К.
Изоморфизмы соболевских пространств на римановых многообразиях и квазиконформные отображения
Сибирский математический журнал. 2019. Т.60. №5. С.996-1034. DOI: 10.33048/smzh.2019.60.503 OpenAlex
Изоморфизмы соболевских пространств на римановых многообразиях и квазиконформные отображения
Сибирский математический журнал. 2019. Т.60. №5. С.996-1034. DOI: 10.33048/smzh.2019.60.503 OpenAlex
Dates:
| Submitted: | Mar 27, 2019 |
| Accepted: | May 15, 2019 |
Identifiers:
| Web of science: | WOS:000488948900003 |
| Scopus: | 2-s2.0-85073390252 |
| OpenAlex: | W2978813232 |