The principle of subordination applied to functions of several variables

Ted Joe Suffridge

Vol. 33 (1970), No. 1, 241–248

DOI: 10.2140/pjm.1970.33.241

Abstract

In this paper we consider univalent maps of domains in Cⁿ(n ≧ 2). Let P be a polydisk in Cⁿ. We find necessary and sufficient conditions that a function f : P−→ Cⁿ be univalent and map the polydisk P onto a starlike or a convex domain. We also consider maps from

(1)

into Cⁿ and give necessary and sufficient conditions that such a map have starlike or convex image.

Mathematical Subject Classification

Primary: 32.60

Milestones

Received: 19 May 1969

Published: 1 April 1970