Biholomorphic convex mappings of ball in ℂⁿ

Sheng Gong, Shi Kun Wang and Qi Huang Yu

Vol. 161 (1993), No. 2, 287–306

DOI: 10.2140/pjm.1993.161.287

Abstract

Biholomorphic convex mappings from unit hall in ℂⁿ into ℂⁿ are studied in this paper. A Schwartz type lemma for the class of mappings and a necessary and sufficient condition under which a holomorphic mapping is biholomorphic and convex are established. The results are used to describe some characteristics of the image of the class of mappings.

Mathematical Subject Classification 2000

Primary: 32H02

Secondary: 30C45, 32A30

Milestones

Received: 29 October 1991

Revised: 29 April 1992

Published: 1 December 1993