On mapping an n-ball into an (n + 1)-ball in complex spaces

Sidney Martin Webster

Vol. 81 (1979), No. 1, 267–272

DOI: 10.2140/pjm.1979.81.267

Abstract

This paper is concerned with proper holomorphic mappings from the unit n-ball Bⁿ in complex n-space Cⁿ into the unit (n + 1)-ball in Cⁿ⁺¹. It will be shown that if such a mapping f is sufficiently regular at the boundary then the image of f lies in a complex hyperplane, provided n ≧ 3.

Mathematical Subject Classification 2000

Primary: 32E35

Secondary: 32F25, 32H99

Milestones

Received: 17 May 1978

Revised: 8 September 1978

Published: 1 March 1979