Conformal metrics of prescribed scalar curvature on 4-manifolds: the degree zero case
type: Item
instance of: scholarly article
title: Conformal metrics of prescribed scalar curvature on 4-manifolds: the degree zero case
zbMATH Open document ID: 1384.35035
author: Hichem Chtioui
author: Mohameden Ould Ahmedou
published in: Arabian Journal of Mathematics
publication date: 2018-01-05T00:00:00Z
review text: Given a compact, \(4\)-dimensional Riemannian manifold \((M^4,g_0)\) with positive scalar curvature \(R_{g_0},\) and a function \(K\in C^2,\) the prescribed scalar curvature problem consists of finding a metric \(g,\) conformally related to \(g_0,\) such that the scalar curvature of \((M, g)\) equals \(K.\) Setting \(g = u^2 g_0,\) this leads to the problem \[ L_{g_0}u=K u^3,\quad u>0\;\text{on}\;M^4, \] where \(L_{g_0}\) stands for the conformal Laplacian \(-\Delta_{g_0}+1/6.\) The authors derive existence results for the above problem that generalize in some sense these already known in the literature. The technique applied relies on estimates for the Morse index of solutions.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 6822574
zbMATH Keywords: prescribed scalar curvature
zbMATH Keywords: conformal metric
zbMATH Keywords: Morse index
MaRDI profile type: Publication
full work available at URL: s40065-017-0169-1
OpenAlex ID: W1661171073
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Wikidata QID: Q59528028
DOI: 10.1007/S40065-017-0169-1
description: scientific article; zbMATH DE number 6822574