Proof of the positive mass conjecture
type: Item
instance of: scholarly article
title: Proof of the positive mass conjecture
zbMATH Open document ID: 1112.53029
author: Thierry Aubin
published in: Journal of Functional Analysis
publication date: 2007-01-16T00:00:00Z
review text: Let \((V_n, g)\), \(n>2\), be a compact Riemannian manifold. If the conformal Laplacian \(L\) is invertible, the author shows under necessary hypotheses, that if the Green function \(G_L\) of \(L\) is of the form \(G_L(P, Q)=\frac{1}{n-2}\omega_{n-1}r^{n-2}+H(P, Q)\), where \(r=d(P,Q)\), with \(H(P, Q)\) bounded on \(V\), then \[ \lim_{r\to 0}r^{1-n}\int_{\partial B_P(r)}H(P,Q)\,d\sigma(Q)>0. \] From this theorem the author deduces theorems on the positive mass and on the \(C^0\)-compactness of the set of the solutions of the Yamabe equation.
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 53C80
zbMATH DE Number: 5116355
zbMATH Keywords: positive mass
zbMATH Keywords: conformal Laplacian
zbMATH Keywords: Green function
reviewed by: Witold Mozgawa
MaRDI profile type: Publication
full work available at URL: j.jfa.2006.05.001
OpenAlex ID: W2052667527
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DOI: 10.1016/J.JFA.2006.05.001
description: scientific article; zbMATH DE number 5116355