On the Gauss map of an area-minimizing hypersurface
type: Item
instance of: scholarly article
title: On the Gauss map of an area-minimizing hypersurface
zbMATH Open document ID: 0548.53051
author: Bruce Solomon
published in: Journal of Differential Geometry
publication date: 1984-01-01T00:00:00Z
review text: Let S be an area-minimizing hypersurface of \({\mathbb{R}}^ N\). In the 1960's it was discovered that the dimensional restriction \(N<8\) guarantees to S several very strong properties which fail to hold as soon as \(N\geq 8\). The most important two of these properties are the interior regularity and the Bernstein property. In the present paper the author shows that the dimensional hypothesis \(N<8\) can be replaced by a different condition which involves the topology and the Gauss image of S and which guarantees both properties independent of dimension. In the case of minimal surfaces a similar condition on the Gauss map appeared in a conjecture of Nirenberg which was proved by R. Osserman.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 57R42
zbMATH DE Number: 3874158
zbMATH Keywords: area-minimizing hypersurface
zbMATH Keywords: interior regularity
zbMATH Keywords: Bernstein property
zbMATH Keywords: Gauss map
Wikidata QID: Q115187828
reviewed by: Fritz Gackstatter
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214438429
OpenAlex ID: W1515486929
DOI: 10.4310/JDG/1214438429
description: scientific article; zbMATH DE number 3874158