Isomorphisms of Sobolev Spaces on Riemannian Manifolds and Quasiconformal Mappings
- Авторлар: Vodopyanov S.1
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Мекемелер:
- Sobolev Institute of Mathematics
- Шығарылым: Том 60, № 5 (2019)
- Беттер: 774-804
- Бөлім: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172620
- DOI: https://doi.org/10.1134/S0037446619050033
- ID: 172620
Дәйексөз келтіру
Аннотация
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.
Негізгі сөздер
Авторлар туралы
S. Vodopyanov
Sobolev Institute of Mathematics
Хат алмасуға жауапты Автор.
Email: vodopis@math.nsc.ru
Ресей, Novosibirsk