Erratum to: On the first eigenvalue of the linearized operator of the \(r\)-th mean curvature of a hypersurface
type: Item
instance of: scholarly article
title: Erratum to: On the first eigenvalue of the linearized operator of the \(r\)-th mean curvature of a hypersurface
zbMATH Open document ID: 0822.53035
DOI: 10.1007/BF00774572
author: Hilário Alencar
author: Harold Rosenberg
author: Manfredo P. do Carmo
published in: Annals of Global Analysis and Geometry
publication date: 1995-07-13T00:00:00Z
review text: The proof of Theorem 3.1 in [the authors, ibid. 11, No. 4, 387-395 (1993; Zbl 0816.53031)] is incorrect: It is not true that the maps \((\widetilde {X}, x) \mapsto (T \widetilde{X},x)\) are isometries of \(\mathbb{H}^{m + 1}\), \(T\) a translation of \(\mathbb{R}^{m+1}\). To correct this, the test functions introduced in [\textit{J. L. Barbosa, J. Eschenburg} and the second author, Math. Z. 197, No. 1, 123-138 (1988; Zbl 0653.53045)] are used.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 761183
zbMATH Keywords: Reilly's inequality
zbMATH Keywords: first eigenvalue
zbMATH Keywords: Laplacian
zbMATH Keywords: higher-order curvature
zbMATH Keywords: \(r\)-stable submanifolds
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 761183