Bulletin of the Belgian Mathematical Society - Simon Stevin

The asymptotical case of certain quasiconformal extension results for holomorphic mappings in $\mathbb{C}^n$

Paula Curt and Gabriela Kohr

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Abstract

Let $f(z,t)$ be a non-normalized subordination chain and assume that $f(\cdot,t)$ is $K$-quasiregular on $B^n$ for $t\in [0,\alpha]$. In this paper we obtain a sufficient condition for $f(\cdot,0)$ to be extended to a quasiconformal homeomorphism of $\overline{\mathbb{R}}^{2n}$ onto $\overline{\mathbb{R}}^{2n}$. Finally we obtain certain applications of this result. One of these applications can be considered the asymptotical case of the $n$-dimensional version of the well known quasiconformal extension result due to Ahlfors and Becker.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 4 (2007), 653-667.

Dates
First available in Project Euclid: 15 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1195157134

Digital Object Identifier
doi:10.36045/bbms/1195157134

Mathematical Reviews number (MathSciNet)
MR2384461

Zentralblatt MATH identifier
1135.32017

Subjects
Primary: 32H 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

Keywords
biholomorphic mapping Loewner differential equation Loewner chain subordination chain subordination quasiregular mapping quasiconformal mapping quasiconformal extension

Citation

Curt, Paula; Kohr, Gabriela. The asymptotical case of certain quasiconformal extension results for holomorphic mappings in $\mathbb{C}^n$. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 4, 653--667. doi:10.36045/bbms/1195157134. https://projecteuclid.org/euclid.bbms/1195157134


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