The maximum principle for hypersurfaces with vanishing curvature functions
type: Item
instance of: scholarly article
title: The maximum principle for hypersurfaces with vanishing curvature functions
zbMATH Open document ID: 0821.53007
author: Maria Luiza Leite
author: Jorge Hounie
published in: Journal of Differential Geometry
publication date: 1995-07-13T00:00:00Z
review text: We extend the maximum principle, known for hypersurfaces of Euclidean \((n+1)\)-space with positive constant curvature function \(\sigma_ k = c > 0\), to a generic class of hypersurfaces with vanishing curvature \(\sigma_ k = 0\), \(1 \leq k < n\). This allows the application of Alexandrov reflection method to this class of hypersurfaces, yielding certain symmetry and uniqueness properties that were known for minimal surfaces.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 761163
zbMATH Keywords: maximum principle
zbMATH Keywords: hypersurfaces with vanishing curvature
zbMATH Keywords: Alexandrov reflection
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214456216
OpenAlex ID: W1589672014
Wikidata QID: Q115178697
DOI: 10.4310/JDG/1214456216
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description: scientific article; zbMATH DE number 761163