Branched immersions between 2-manifolds of higher topological type

John D. Elwin and Donald R. Short

Vol. 58 (1975), No. 2, 361–370

DOI: 10.2140/pjm.1975.58.361

Abstract

In this paper, branched immersions between compact orientable 2-manifolds are considered. Branched immersions are smooth maps whose only singularities are branch points, i.e., points of the domain where the map is locally topologically equivalent to z → z^r(r = 2,3,⋯). Originally these maps were studied in connection with Douglas’ solution to Plateau’s problem.

The maps considered here are required to satisfy natural boundary hypothesis which have been motivated by minimal surface studles. The main result completely decides the existence question for a branched immersion between compact orientable 2-manifolds with or without boundary.

Mathematical Subject Classification 2000

Primary: 53A10

Milestones

Received: 12 June 1974

Revised: 27 August 1974

Published: 1 June 1975