ON MORI’S THEOREM FOR QUASICONFORMAL MAPS IN THE n-SPACE
نویسندگان
چکیده
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 . We give here 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 .
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