First \(\frac{2}{n}\)-stability eigenvalue of singular minimal hypersurfaces in space forms
type: Item
instance of: scholarly article
title: First \(\frac{2}{n}\)-stability eigenvalue of singular minimal hypersurfaces in space forms
zbMATH Open document ID: 1505.53011
author: Ha Tuan Dung
author: Nguyen Thac Dung
author: Juncheol Pyo
published in: Annals of Global Analysis and Geometry
publication date: 2022-10-24T00:00:00Z
review text: If \(M\) is a minimal hypersurface in a space form \(\overline{M}^{n+1}(c)\) and \(A\) is its second fundamental form, then \(M\) is said to be \(\frac2n\)-\textit{stable} when for all \(f\in C^\infty_0(M)\) the integral \[\int_M (\| \nabla f\|^2 - \frac{n-2}{n}(\| A\|^2 + cn)f^2)\] is nonnegative. In this paper, the authors study such stability on singular minimal hypersurfaces in space forms and provide a characterization of catenoids in space forms in terms of this stability.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 7606041
zbMATH Keywords: catenoids
zbMATH Keywords: stability
zbMATH Keywords: minimal hypersurfaces
reviewed by: Paweł Walczak
MaRDI profile type: Publication
full work available at URL: s10455-022-09880-y
OpenAlex ID: W4307361853
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DOI: 10.1007/S10455-022-09880-Y
description: scientific article; zbMATH DE number 7606041