On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations
type: Item
instance of: scholarly article
title: On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations
zbMATH Open document ID: 0764.53027
DOI: 10.1007/BF02096944
author: Lars Andersson
author: Helmut Friedrich
author: Piotr T. Chrúsciel
published in: Communications in Mathematical Physics
publication date: 1993-01-17T00:00:00Z
review text: Yamabe's problem in Riemannian geometry -- to find a conformal transformation which sends the scalar curvature \(R\) to a constant \(\widetilde R\) -- is solved here for negative \(\widetilde R\) and 3- dimensional, orientable, compact, smooth manifolds \(M\) with boundary \(\partial M\). Additionally, criteria for conformal compactification are presented and some of the results hold for any dimension \(n\) of \(M\). The improvements concern also the analytical methods: weighted Hölder spaces, asymptotic expansions,... The authors discuss the motivation by the initial value problem to Einstein's equations, too.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 58J05
zbMATH DE Number: 97875
zbMATH Keywords: Yamabe's problem
zbMATH Keywords: conformal compactification
zbMATH Keywords: weighted Hölder spaces
zbMATH Keywords: asymptotic expansions
reviewed by: Rainer Schimming
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 97875