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.
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To Yu. G. Reshetnyak on the occasion of his 90th birthday.
Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 5, pp. 996–1034.
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).
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Vodopyanov, S.K. Isomorphisms of Sobolev Spaces on Riemannian Manifolds and Quasiconformal Mappings. Sib Math J 60, 774–804 (2019). https://doi.org/10.1134/S0037446619050033
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DOI: https://doi.org/10.1134/S0037446619050033