The scalar curvature equation on 2- and 3-spheres
type: Item
instance of: scholarly article
title: The scalar curvature equation on 2- and 3-spheres
zbMATH Open document ID: 0822.35043
DOI: 10.1007/BF01191617
author: Matthew J. Gursky
author: Paul C. Yang
author: Sun-Yung Alice Chang
published in: Calculus of Variations and Partial Differential Equations
publication date: 1995-10-09T00:00:00Z
review text: The problem of finding a metric on \(S^ n\) of prescribed scalar curvature \(R\) which is conformally equivalent to the standard metric has received a great deal of attention, but is still not completely resolved. It is well known that the problem reduces to solving a certain nonlinear elliptic equation on \(S^ n\). Here the authors derive some a priori estimates for solutions of this equation in the cases \(n=2,3\) under appropriate conditions on \(R\). This enables them to use the continuity method to obtain some existence results which generalize those of \textit{S.-Y. A. Chang} and \textit{P. C. Yang} [Acta Math. 159, 215-259 (1987; Zbl 0636.53053)] for \(S^ 2\), and \textit{A. Bahri} and \textit{J. M. Coron} [J. Funct. Anal. 95, No. 1, 106-172 (1991; Zbl 0722.53032)] for \(S^ 3\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 509965
zbMATH Keywords: metric of prescribed scalar curvature
zbMATH Keywords: continuity method
Wikidata QID: Q115393940
reviewed by: John Urbas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 509965