Isomorphisms of Sobolev Spaces on Riemannian Manifolds and Quasiconformal Mappings
- Authors: Vodopyanov S.K.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 60, No 5 (2019)
- Pages: 774-804
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172620
- DOI: https://doi.org/10.1134/S0037446619050033
- ID: 172620
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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.
About the authors
S. K. Vodopyanov
Sobolev Institute of Mathematics
Author for correspondence.
Email: vodopis@math.nsc.ru
Russian Federation, Novosibirsk