On Mori's theorem for quasiconformal maps in the n-space

: Bhayo B, Vuorinen M

Publisher: AMER MATHEMATICAL SOC

: 2011

: Transactions of the American Mathematical Society

: T AM MATH SOC

: 11

: 363

: 11

: 5703

: 5719

: 17

: 0002-9947

DOI: https://doi.org/10.1090/S0002-9947-2011-05281-5

: http://api.elsevier.com/content/abstract/scopus_id:79960794592

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.