On compactness of isospectral conformal metrics of \(4\)-sphere
type: Item
instance of: scholarly article
title: On compactness of isospectral conformal metrics of \(4\)-sphere
zbMATH Open document ID: 0842.53010
author: Xingwang Xu
published in: Communications in Analysis and Geometry
publication date: 1996-07-28T00:00:00Z
review text: Let \((S^4, g_0)\) be the 4-dimensional sphere with the standard metric. Let \(g= u^2 g_0\) be a conformally equivalent metric. The author shows that if the scalar curvature of \(g\) is near constant in the \(L^2\) sense, then the set of conformal metrics which are isospectral to \(g\) is compact in the \(C^\infty\) topology modulo gauge equivalence. The conformal group is noncompact, so it is necessary to work modulo gauge equivalence. The author notes that the condition that the scalar curvature of \(g\) is near constant does not imply that \(g\) is \(C^0\) close to the standard metric modulo gauge equivalence. This paper generalizes work of Osgood, Phillips, and Sarnak in dimension 2 and of Brooks, Chang, Perry, and Yang in dimension 3.
reviewed by: Peter B. Gilkey
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 856920
zbMATH Keywords: four-sphere
zbMATH Keywords: isospectral conformal metrics
zbMATH Keywords: near constant scalar curvature
zbMATH Keywords: gauge equivalence
MaRDI profile type: Publication
full work available at URL: cag.1995.v3.n2.a6
OpenAlex ID: W2715008841
Wikidata QID: Q125801223
DOI: 10.4310/CAG.1995.V3.N2.A6
description: scientific article; zbMATH DE number 856920