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.
The results in § 5.2 were obtained within the framework of a state assignment of the Ministry of Education and Science of the Russian Federation (grant no. 1.3087.2017/4.6) and the results in § 5.1 we obtained with the support of the Russian Foundation for Basic Research (grant no. 17-01-00801-a).
\Bibitem{Vod19}
\by S.~K.~Vodopyanov
\paper Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds
\jour Sb. Math.
\yr 2019
\vol 210
\issue 1
\pages 59--104
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This publication is cited in the following 14 articles:
S. K. Vodopyanov, S. V. Pavlov, “Funktsionalnye svoistva predelov sobolevskikh gomeomorfizmov s integriruemym iskazheniem”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy
matematicheskogo obrazovaniya, SMFN, 70, no. 2, Rossiiskii universitet druzhby narodov, M., 2024, 215–236
S. K. Vodopyanov, S. V. Pavlov, “O granichnykh znacheniyakh v geometricheskoi teorii funktsii v oblastyakh s podvizhnymi granitsami”, Sib. matem. zhurn., 65:3 (2024), 489–516
S. K. Vodopyanov, S. V. Pavlov, “Boundary Values in the Geometric Function Theory in Domains with Moving Boundaries”, Sib Math J, 65:3 (2024), 552
S. K. Vodopyanov, “The Geometric Function Properties of the Limits of ACL-Mappings with Integrable Distortion”, Sib Math J, 65:5 (2024), 1026
S. K. Vodopyanov, “Funktsionalno-geometricheskie svoistva predelov ACL-otobrazhenii s integriruemym iskazheniem”, Sib. matem. zhurn., 65:5 (2024), 820–840
S. K. Vodopyanov, “Composition operators in Sobolev spaces on Riemannian manifolds”, Siberian Math. J., 65:6 (2024), 1305–1326
S. K. Vodopyanov, S. V. Pavlov, “Functional Properties of Limits of Sobolev Homeomorphisms with Integrable Distortion”, J Math Sci, 2024
Izv. Math., 87:4 (2023), 683–725
S. K. Vodopyanov, “Coincidence of set functions in quasiconformal analysis”, Sb. Math., 213:9 (2022), 1157–1186
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
S. K. Vodopyanov, “Two-weighted composition operators on Sobolev spaces and quasiconformal analysis”, J. Math. Sci., 266:3 (2022), 491–509
S. K. Vodopyanov, “On the equivalence of two approaches to problems of quasiconformal analysis”, Siberian Math. J., 62:6 (2021), 1010–1025
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
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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