On false branch points of incompressible branched immersions
type: Item
instance of: scholarly article
title: On false branch points of incompressible branched immersions
zbMATH Open document ID: 0701.53009
DOI: 10.1007/BF01168372
author: Robert Gulliver
author: F. Tomi
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155382
review text: Branched minimal immersions appear naturally as solutions of Plateau's problem. A basic question is to decide when such an immersion is in fact unbranched. If the minimal surface is area minimizing in a three- manifold, we have a satisfactory answer from the results of Osserman, Alt and Gulliver. In this paper the authors obtain a regularity result under assumptions related to incompressibility of the surface. More precisely, given a branched minimal immersion f from a Riemann surface with boundary M into a Riemannian manifold N, if f induces an isomorphism between the fundamental groups of M and N, and is one-to-one on the boundary of M, then f has no ramified points.
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 4149053
zbMATH Keywords: Branched minimal immersions
zbMATH Keywords: area minimizing
zbMATH Keywords: regularity result
zbMATH Keywords: incompressibility
MaRDI profile type: Publication
cites work: Verzweigungspunkte von H-Flächen. I
cites work: Branched immersions onto compact orientable surfaces
cites work: Branched immersions between 2-manifolds of higher topological type
cites work: Regularity of minimizing surfaces of prescribed mean curvature
cites work: Finiteness of the ramified set for branched immersions of surfaces
cites work: A Theory of Branched Immersions of Surfaces
cites work: Conformal mappings and the Plateau-Douglas problem in Riemannian manifolds.
cites work: Q3314604
cites work: Q5534009
cites work: Q5510566
cites work: A proof of the regularity everywhere of the classical solution to Plateau's problem
cites work: Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
cites work: Existence theorems for minimal surfaces of nonzero genus spanning a contour
description: scientific article; zbMATH DE number 4149053