Scalar curvature and conformal deformations of noncompact Riemannian manifolds
type: Item
instance of: scholarly article
title: Scalar curvature and conformal deformations of noncompact Riemannian manifolds
zbMATH Open document ID: 0899.53033
DOI: 10.1007/PL00004619
author: Andrea Ratto
author: M. Rigoli
author: Laurent Véron
published in: Mathematische Zeitschrift
publication date: 1998-11-15T00:00:00Z
review text: The main aim of this paper is to study the following question. Problem. Let \(K\in C^\infty (M)\), where \((M,g)\) is an \(m\)-dimensional, connected, complete, noncompact Riemannian manifold, \(m\geq 3\). Does there exist a conformal deformation \(g_u\) \((g_u= u^{4/(m-2)}g\), \(u\) a smooth, positive function on \(M)\) of \(g\) such that \(K\) is the scalar curvature of \(g_u\) and \(g_u\) is complete? Essentially, the authors study in detail the case where \(K(x)\) is negative outside a compact set. They refine the results obtained by Avilès-McOwen, Jin, Gui-Wang and establish some uniqueness theorems as well.
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 1057298
zbMATH Keywords: noncompact manifold
zbMATH Keywords: conformal deformation
zbMATH Keywords: scalar curvature
Wikidata QID: Q115390574
reviewed by: Stana Nikčević
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1057298