TY - JOUR

T1 - Isomorphisms of Sobolev Spaces on Riemannian Manifolds and Quasiconformal Mappings

AU - Vodopyanov, S. K.

N1 - Publisher Copyright: © 2019, Pleiades Publishing, Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - composition operator

KW - quasiconformal mapping

KW - Riemannian manifold

KW - Sobolev space

UR - http://www.scopus.com/inward/record.url?scp=85073390252&partnerID=8YFLogxK

U2 - 10.1134/S0037446619050033

DO - 10.1134/S0037446619050033

M3 - Article

AN - SCOPUS:85073390252

VL - 60

SP - 774

EP - 804

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -