The asymptotical case of certain quasiconformal extension results for holomorphic mappings in $\mathbb{C}^n$
Curt, Paula ; Kohr, Gabriela
Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 653-667 / Harvested from Project Euclid
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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.
Publié le : 2007-11-14
Classification:  biholomorphic mapping,  Loewner differential equation,  Loewner chain,  subordination chain,  subordination,  quasiregular mapping,  quasiconformal mapping,  quasiconformal extension,  32H,  30C45 
@article{1195157134,
     author = {Curt, Paula and Kohr, Gabriela},
     title = {The asymptotical case of certain quasiconformal extension results
for holomorphic mappings in $\mathbb{C}^n$},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 653-667},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1195157134}
}

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, Tome 13 (2007) no. 5, pp.  653-667. http://gdmltest.u-ga.fr/item/1195157134/