Addendum: Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature
type: Item
instance of: scholarly article
title: Addendum: Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature
zbMATH Open document ID: 0861.53036
DOI: 10.2307/2118578
published in: Annals of Mathematics. Second Series
publication date: 1994-10-24T00:00:00Z
review text: In the author's paper [ibid. 136, No. 1, 1-50 (1992; Zbl 0766.53033)] the first eigenvalue \(\lambda_1(B)\) of the problem \[ \begin{cases} Lf=0 & \text{on \(M\),}\\ Bf+\lambda_1(B)f=0 & \text{on \(\partial M\),}\end{cases} \] where \((L,B)\) is the conformal Laplacian, was considered, under the tacit assumption that \(\lambda_1(B)\) is finite. This addendum discusses this question in detail; it is remarked that only Theorem 2 and Propositions 1.4 and 1.5 in above paper need the assumption on finiteness of \(\lambda_1(B)\) whereas the other statements remain correct without this explicit assumption.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 58J32
zbMATH DE Number: 640759
zbMATH Keywords: first eigenvalue
zbMATH Keywords: conformal Laplacian
Wikidata QID: Q115229223
author: José F. Escobar
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2118578
OpenAlex ID: W2313008578
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description: scientific article; zbMATH DE number 640759