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Univalence criterion and quasiconformal extension of holomorphic mappings

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Abstract

In this paper we are concerned with solutions, in particular with the univalent solutions, of the Loewner differential equation associated with non-normalized subordination chains on the Euclidean unit ball B in \({\mathbb{C}^n}\). We also give applications to univalence conditions and quasiconformal extensions to \({\mathbb{C}^n}\) of holomorphic mappings on B. Finally we consider the asymptotical case of these results. The results in this paper are complete generalizations to higher dimensions of well known results due to Becker. They improve and extend previous sufficient conditions for univalence and quasiconformal extension to \({\mathbb{C}^n}\) of holomorphic mappings on B.

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Authors and Affiliations

  1. Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, Higashi-ku, Fukuoka, 813-8503, Japan

    Hidetaka Hamada

  2. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 400084, Cluj-Napoca, Romania

    Gabriela Kohr

Authors
  1. Hidetaka Hamada
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  2. Gabriela Kohr
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Correspondence to Hidetaka Hamada.

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Hamada, H., Kohr, G. Univalence criterion and quasiconformal extension of holomorphic mappings. manuscripta math. 141, 195–209 (2013). https://doi.org/10.1007/s00229-012-0568-8

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