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On the Bloch Constant for Κ-Quasiconformal Mappings in Several Complex Variables

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Abstract

We study the Bloch constant for K-quasiconformal holomorphic mappings of the unit ball B of C n into C n. The final result we prove in this paper is: If f is a K-quasiconformal holomorphic mapping of B into C n such that det(f'(0)) = 1, then f(B) contains a schlicht ball of radius at least

$$ {\left( {C_{n} K} \right)}^{{1 - n}} {\int\limits_0^1 {\frac{{{\left( {1 + t} \right)}^{{n - 1}} }} {{{\left( {1 - t} \right)}^{2} }}} }\exp {\left\{ {\frac{{ - {\left( {n + 1} \right)}t}} {{1 - t}}} \right\}}dt, $$

where C n > 1 is a constant depending on n only, and \( C_{n} \to {\sqrt {10} } \) as n→ ∞.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China

    J. Y. Gamaliel & Huai Hui Chen

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  1. J. Y. Gamaliel
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  2. Huai Hui Chen
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Correspondence to Huai Hui Chen.

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Research supported in part by NSFC (China) and JNSF (Jiangsu).

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Gamaliel, J.Y., Chen, H.H. On the Bloch Constant for Κ-Quasiconformal Mappings in Several Complex Variables. Acta Math Sinica 17, 237–242 (2001). https://doi.org/10.1007/s101140100105

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  • DOI: https://doi.org/10.1007/s101140100105

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