On the singular structure of two-dimensional area minimizing surfaces in \({\mathbb{R}}^ n\)
type: Item
instance of: scholarly article
title: On the singular structure of two-dimensional area minimizing surfaces in \({\mathbb{R}}^ n\)
zbMATH Open document ID: 0549.49029
DOI: 10.1007/BF01456413
author: Frank Morgan
published in: Mathematische Annalen
publication date: 1982-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/182868
review text: The author investigates which combinations of planes through the origin minimize area and applies this theory to the tangent cone to any area minimizing surface. The main results are: (1) ''A tangent cone to an oriented two-dimensional area minimizing surface in \(R^ n\) consists entirely of complex planes'', (2) ''In some neighbourhood of an interior singular point a, an oriented two-dimensional area minimizing surface in \(R^ n\) consists of at most n/2 manifolds, which intersect orthogonally at a''.
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 49Q15
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 3876062
zbMATH Keywords: singular structure
zbMATH Keywords: tangent cone
zbMATH Keywords: area minimizing surface
reviewed by: Constantin Udrişte
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3876062