Quasiconformality of the injective mappings transforming spheres to quasispheres
- Authors: Aseev V.V.1
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Affiliations:
- Sobolev Institute of Mathematics Novosibirsk State University
- Issue: Vol 57, No 5 (2016)
- Pages: 747-753
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170665
- DOI: https://doi.org/10.1134/S0037446616050013
- ID: 170665
Cite item
Abstract
We prove that every injective mapping of a domain \(D \subset \overline {{\mathbb{R}^n}} \) transforming spheres Σ ⊂ D to K-quasispheres (the images of spheres under K-quasiconformal automorphisms of \(\overline {{\mathbb{R}^n}} \)) is K′-quasiconformal with K′ depending only on K and tending to 1 as K → 1. This is a quasiconformal analog of the classical Carathéodory Theorem on the Möbius property of an injective mapping of a domain D ⊂ Rn which sends spheres to spheres.
About the authors
V. V. Aseev
Sobolev Institute of Mathematics Novosibirsk State University
Author for correspondence.
Email: btp@math.nsc.ru
Russian Federation, Novosibirsk