The first eigenvalue of the Laplacian of an isoparametric minimal hypersurface in a unit sphere
type: Item
instance of: scholarly article
title: The first eigenvalue of the Laplacian of an isoparametric minimal hypersurface in a unit sphere
zbMATH Open document ID: 0652.53039
DOI: 10.1007/BF01159810
author: Hideo Muto
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183749
review text: This is an interesting paper about the following open problem: Let x: \(M_{n-1}\to S^ n(1)\) be a closed minimal hypersurface in the unit n- sphere. The first eigenvalue \(\lambda_ 1\) of the Laplacian satisfies \(\lambda_ 1\leq n-1\) (Takahashi). For which manifolds is \(\lambda_ 1=n-1?\quad -\) The author gives partial answers for classes of isoparametric minimal hypersurfaces (and lower estimates also for higher eigenvalues \(\lambda_ k)\).
reviewed by: Udo Simon
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 58J60
zbMATH DE Number: 4063987
zbMATH Keywords: isoparametric hypersurfaces
zbMATH Keywords: minimal hypersurface
zbMATH Keywords: unit n-sphere
zbMATH Keywords: first eigenvalue
zbMATH Keywords: Laplacian
MaRDI profile type: Publication
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OpenAlex ID: W4244374685
description: scientific article; zbMATH DE number 4063987