The scalar curvature problem on \(S^n\): An approach via Morse theory
type: Item
instance of: scholarly article
title: The scalar curvature problem on \(S^n\): An approach via Morse theory
zbMATH Open document ID: 1012.53035
author: Andrea Malchiodi
published in: Calculus of Variations and Partial Differential Equations
publication date: 2002-09-10T00:00:00Z
review text: In this paper the author proves the existence of positive solutions for the equation \[ -4{n-1 \over n-2 }\Delta u +n(n-1)u = R' u^{{n+2 \over n-2 }} \] on the sphere \(S^n\) (\(n \geq 3\)), where \(\Delta\) denotes the Laplace-Beltrami operator with respect to the standard metric on \(S^n\) and \(R'\) is a small perturbation of a constant. Applying perturbation methods and placing suitable non-degeneracy conditions on the perturbations the author reduces the problem from an infinite-dimensional problem to a finite-dimensional one in order to obtain the existence.
reviewed by: Thomas Hasanis
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1798863
zbMATH Keywords: scalar curvature problem
zbMATH Keywords: partial differential equations
zbMATH Keywords: perturbation methods
MaRDI profile type: Publication
full work available at URL: s005260100110
OpenAlex ID: W236849525
DOI: 10.1007/S005260100110
description: scientific article; zbMATH DE number 1798863