Geodesic
Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds
Sbornik. Mathematics, Tome 210 (2019) no. 1, pp. 59-104

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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.
Keywords: Riemannian manifold, quasi-isometric map, Sobolev space, composition operator. 
@article{SM_2019_210_1_a2,
     author = {S. K. Vodopyanov},
     title = {Admissible changes of variables for {Sobolev} functions on {(sub-)Riemannian} manifolds},
     journal = {Sbornik. Mathematics},
     pages = {59--104},
     publisher = {mathdoc},
     volume = {210},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_1_a2/}
}
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S. K. Vodopyanov. Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. Sbornik. Mathematics, Tome 210 (2019) no. 1, pp. 59-104. http://geodesic.mathdoc.fr/item/SM_2019_210_1_a2/