Global existence and convergence for a higher order flow in conformal geometry
type: Item
instance of: scholarly article
title: Global existence and convergence for a higher order flow in conformal geometry
zbMATH Open document ID: 1042.53016
author: Simon Brendle
published in: Annals of Mathematics. Second Series
publication date: 2003-10-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0404415
review text: The main purpose of this paper is to construct conformal metrics for which the curvature quantity \(Q\) is a constant multiple of a prescribed positive function \(f\) on a compact n-dimensional manifold \(M\). In section 2 the author derives the evolution equation for the conformal factor and the curvature quantity \(Q\), next, in section 3 he shows that the solution is bounded in \(H^{n/2}\). In sections 4 and 5 the author shows that the solution exists for all time, and in section 6 he proves that the evolution equation converges to a stationary solution. Finally, in section 8 he proves a compactness theorem for conformal metrics on \(S^n\) (proposition 1.4).
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 58D25
zbMATH DE Number: 1997278
zbMATH Keywords: conformal geometry
zbMATH Keywords: higher order flow
zbMATH Keywords: evolution equation
zbMATH Keywords: curvature quantity
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
OpenAlex ID: W2113998944
arXiv ID: math/0404415
DOI: 10.4007/ANNALS.2003.158.323
description: scientific article