Convex Subordination Chains in Several Complex Variables

Graham, Ian ; Hamada, Hidetaka ; Kohr, Gabriela ; Pfaltzgraff, John A.

Canadian journal of mathematics, Tome 61 (2009) no. 3, pp. 566-582

Résumé

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 ${{B}^{n}}\backslash \{0\}$ , where $f(z,t)$ is a convex subordination chain over $(0,1)$ .

Détail

DOI : 10.4153/CJM-2009-030-x

Mots-clés : 32H02, 30C45, biholomorphic mapping, convex mapping, convex subordination chain, Loewner chain, subordination.

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