Nonuniqueness and high energy solutions for a conformally invariant scalar equation
type: Item
instance of: scholarly article
title: Nonuniqueness and high energy solutions for a conformally invariant scalar equation
zbMATH Open document ID: 0848.58011
author: Daniel Pollack
published in: Communications in Analysis and Geometry
publication date: 1996-01-22T00:00:00Z
review text: The Yamabe problem asserts that given any compact Riemannian manifold \((M,\overline {g})\) without boundary and of dimension greater than or equal to three, there exists a conformally related metric \(g\), with constant scalar curvature. The author proves the existence of arbitrarily many distinct solutions to the Yamabe problem with constant positive scalar curvature, all lying within a fixed conformal class which is arbitrarily close, in the \(C^0\) topology, to the conformal class of any given metric of positive scalar curvature.
Mathematics Subject Classification ID: 58E11
Mathematics Subject Classification ID: 58D17
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 836424
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: Yamabe invariant
zbMATH Keywords: Yamabe problem
zbMATH Keywords: conformal class
MaRDI profile type: Publication
full work available at URL: cag.1993.v1.n3.a2
OpenAlex ID: W2619662150
DOI: 10.4310/CAG.1993.V1.N3.A2
description: scientific article; zbMATH DE number 836424