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1. CJM 2009 (vol 61 pp. 566)

Graham, Ian; Hamada, Hidetaka; Kohr, Gabriela; Pfaltzgraff, John A.
Convex Subordination Chains in Several Complex Variables
In this paper we study the notion of a convex subordination chain in several complex variables. We obtain certain necessary and sufficient conditions for a mapping to be a convex subordination chain, and we give various examples of convex subordination chains on the Euclidean unit ball in $\mathbb{C}^n$. We also obtain a sufficient condition for injectivity of $f(z/\|z\|,\|z\|)$ on $B^n\setminus\{0\}$, where $f(z,t)$ is a convex subordination chain over $(0,1)$.

Keywords:biholomorphic mapping, convex mapping, convex subordination chain, Loewner chain, subordination
Categories:32H02, 30C45

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