Branched immersions onto compact orientable surfaces

John D. Elwin and Donald R. Short

Vol. 54 (1974), No. 1, 113–122

DOI: 10.2140/pjm.1974.54.113

Abstract

In this paper smooth maps f : Mⁿ → Nⁿ with a zero-dimensional critical set are considered. The singularities of these maps in the case n = 2 are known to be points where f is locally topologically equivalent to z → z^a(d = 2,S,⋯). Originally these singularities were studied in connection with the regularity of Douglas’ solution to Plateau’s problem.

Mathematical Subject Classification

Primary: 57D20

Secondary: 57D40

Milestones

Received: 20 April 1973

Revised: 13 September 1973

Published: 1 September 1974