Loewner chains and quasiconformal extension of holomorphic mappings
Volume 81 / 2003
Annales Polonici Mathematici 81 (2003), 85-100
MSC: 32H02, 30C65.
DOI: 10.4064/ap81-1-8
Abstract
Let $f(z,t)$ be a Loewner chain on the Euclidean unit ball ${B}$ in ${\mathbb C}^n$. Assume that $f(z)=f(z,0)$ is quasiconformal. We give a sufficient condition for $f$ to extend to a quasiconformal homeomorphism of ${\mathbb R}^{2n}$ onto itself.
