Quasi-convergence of model geometries under the Ricci flow
type: Item
instance of: scholarly article
title: Quasi-convergence of model geometries under the Ricci flow
zbMATH Open document ID: 1020.53044
author: Dan Knopf
author: Kevin McLeod
published in: Communications in Analysis and Geometry
publication date: 2003-10-05T00:00:00Z
review text: Let \(g\) and \(h\) be evolving Riemannian metrics on a manifold \(M^n\). In an earlier paper, Knopf formulated the notion of quasi-convergence of \(g\) to \(h\) if for any \(\varepsilon >0\) there exists a time \(t_{\varepsilon}\) such that \(\sup_{M^n \times [t_{\varepsilon}, \infty)} |g-h|_h < \varepsilon\). This is actually an equivalence relation which can be used to classify the asymptotic behavior of Ricci flows which exist for all time. The present paper focuses on the study of quasi-convergence equivalence classes of locally homogeneous metrics for which the Ricci flow exists to infinity. The authors consider the most general families of such metrics by using model geometries \((\chi, \mathcal{G})\), with \(\mathcal{G}\) minimal.
reviewed by: Alina Stancu
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 1833142
zbMATH Keywords: locally homogeneous metrics
zbMATH Keywords: model geometry
zbMATH Keywords: quasi-convergence
zbMATH Keywords: Ricci flow
MaRDI profile type: Publication
Wikidata QID: Q125863722
full work available at URL: cag.2001.v9.n4.a7
OpenAlex ID: W2740057925
DOI: 10.4310/CAG.2001.V9.N4.A7
description: scientific article; zbMATH DE number 1833142