A1 Refereed original research article in a scientific journal
On Mori's theorem for quasiconformal maps in the n-space
Authors: Bhayo B, Vuorinen M
Publisher: AMER MATHEMATICAL SOC
Publication year: 2011
Journal: Transactions of the American Mathematical Society
Journal name in source: Transactions of the American Mathematical Society
Journal acronym: T AM MATH SOC
Number in series: 11
Volume: 363
Issue: 11
First page : 5703
Last page: 5719
Number of pages: 17
ISSN: 0002-9947
DOI: https://doi.org/10.1090/S0002-9947-2011-05281-5
Web address : http://api.elsevier.com/content/abstract/scopus_id:79960794592
Abstract
R. Fehlmann and M. Vuorinen proved in 1988 that Mori's constant M(n,K) for K-quasiconformal maps of the unit ball in Rn onto itself keeping the origin fixed satisfies M(n,K) → 1 when K → 1. Here we give an alternative proof of this fact, with a quantitative upper bound for the constant in terms of elementary functions. Our proof is based on a refinement of a method due to G.D. Anderson and M. K. Vamanamurthy. We also give an explicit version of the Schwarz lemma for quasiconformal self-maps of the unit disk. Some experimental results are provided to compare the various bounds for the Mori constant when n = 2. © 2011 American Mathematical Society.
R. Fehlmann and M. Vuorinen proved in 1988 that Mori's constant M(n,K) for K-quasiconformal maps of the unit ball in Rn onto itself keeping the origin fixed satisfies M(n,K) → 1 when K → 1. Here we give an alternative proof of this fact, with a quantitative upper bound for the constant in terms of elementary functions. Our proof is based on a refinement of a method due to G.D. Anderson and M. K. Vamanamurthy. We also give an explicit version of the Schwarz lemma for quasiconformal self-maps of the unit disk. Some experimental results are provided to compare the various bounds for the Mori constant when n = 2. © 2011 American Mathematical Society.
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