On the branch point index of minimal surfaces
type: Item
instance of: scholarly article
title: On the branch point index of minimal surfaces
zbMATH Open document ID: 1181.49040
author: S. Hildebrandt
author: Anthony J. Tromba
published in: Archiv der Mathematik
publication date: 2009-06-16T00:00:00Z
review text: The authors consider minimal surfaces bounded by smooth Jordan curves (of varying degrees of smoothness). They show that the index of an interior branch point is bounded above by one less than half the maximum number of intersection points of the boundary curve with an affine plane. They observe that the notion of index can be extended to branch points on the boundary if the curve is real analytic by taking an analytic extension of the surface (past the boundary). Furthermore, they give a definition of index for branch points on the boundary even for sufficiently smooth boundary curves under the condition that the curvature and torsion of the boundary curve never vanish and they bound this index above and below. Finally, the authors show that the number of total branch points is finite.
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 5565267
zbMATH Keywords: minimal surfaces
zbMATH Keywords: branch points
zbMATH Keywords: index
reviewed by: John Oprea
MaRDI profile type: Publication
full work available at URL: s00013-009-3146-x
OpenAlex ID: W2068578248
DOI: 10.1007/S00013-009-3146-X
description: scientific article; zbMATH DE number 5565267