Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. (January 2019)

• Record Type: Journal Article
• Authors: Vodopyanov, S. K.
• Is Part Of: Sbornik. Volume 210:Number 1(2019)
• Page Start: 59
• Page End: 104
• Publication Date: 2019-01
• Subjects: 46E35 -- 58C25; 30C65; Riemannian manifold -- quasi-isometric map -- Sobolev space -- composition operator; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM8899
• Languages: English
• ISSNs: 1064-5616

Abstract

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.