Bahri-Coron type theorem for the scalar curvature problem on high dimensional spheres
type: Item
instance of: scholarly article
title: Bahri-Coron type theorem for the scalar curvature problem on high dimensional spheres
zbMATH Open document ID: 1258.35072
author: Mohamed Ben Ayed
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2012-03-08T00:00:00Z
review text: In this paper a conformal scalar curvature equation on the standard sphere of dimension greater than or equal to seven is considered. The author investigates the case when the scalar curvature of the conformal metric is flat near some critical points and can have some nondegenerate critical points. Using the theory of critical points at infinity, the author proves existence results in a form of a Bahri-Coron theorem.
reviewed by: Marek Galewski
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 6012915
zbMATH Keywords: scalar curvature
zbMATH Keywords: critical point at infinity
zbMATH Keywords: critical exponent
zbMATH Keywords: pseudo-gradient
MaRDI profile type: Publication
full work available at URL: s10231-010-0176-8
OpenAlex ID: W2015442442
cites work: Perturbation of \(\Delta u+u^{(N+2)/(N-2)}=0\), the scalar curvature problem in \(\mathbb{R}^N\), and related topics
cites work: Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire
cites work: Algebraic topology methods for the prescribed scalar curvature problem
cites work: Q3992582
cites work: An invariant for Yamabe-type flows with applications to scalar-curvature problems in high dimension
cites work: The scalar-curvature problem on the standard three-dimensional sphere
cites work: Periodic solutions of Hamiltonian systems of 3-body type
cites work: On the prescribed scalar curvature problem on 4-manifolds
cites work: Multiplicity results for the prescribed scalar curvature on low spheres
cites work: A perturbation result in prescribing scalar curvature on \(S^ n\)
cites work: Estimates of the conformal scalar curvature equation via the method of moving planes
cites work: Estimate of the conformal scalar curvature equation via the method of moving planes. II
cites work: Prescribing scalar curvature on \(S^ N\). I: A priori estimates.
cites work: Conformal metrics with prescribed scalar curvature
cites work: Scalar curvature and conformal deformation of Riemannian structure
cites work: Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
cites work: Q5687306
cites work: The concentration-compactness principle in the calculus of variations. The limit case. I
cites work: Q5543303
cites work: Prescribing scalar curvature on \(S^{3}\)
cites work: Prescribed scalar curvature on the \(n\)-sphere
cites work: A global compactness result for elliptic boundary value problems involving limiting nonlinearities
DOI: 10.1007/S10231-010-0176-8
Recommended article: On the Scalar Curvature Equations in high dimension
Recommended article: The scalar-curvature problem on higher-dimensional spheres
Recommended article: The sphere theorems for manifolds with positive scalar curvature
Recommended article: A sphere theorem for Bach-flat manifolds with positive constant scalar curvature
Recommended article: On the scalar curvature of compact hypersurfaces
Recommended article: On the \(P\)-scalar curvature
Recommended article: On isotropic Berwald scalar curvature
Recommended article: The scalar curvature equation on 2- and 3-spheres
Recommended article: Bernstein-type theorems in hypersurfaces with constant mean curvature
Recommended article: Multiplicity results for the prescribed scalar curvature on low spheres
description: scientific article; zbMATH DE number 6012915