CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Convex Subordination Chains in Several Complex Variables

  Published:2009-06-01
 Printed: Jun 2009
  • Ian Graham
  • Hidetaka Hamada
  • Gabriela Kohr
  • John A. Pfaltzgraff
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

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 biholomorphic mapping, convex mapping, convex subordination chain, Loewner chain, subordination
MSC Classifications: 32H02, 30C45 show english descriptions Holomorphic mappings, (holomorphic) embeddings and related questions
Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
32H02 - Holomorphic mappings, (holomorphic) embeddings and related questions
30C45 - Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/