Stability of Euclidean space under Ricci flow

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dc.creatorSchnürer, Oliver C.
dc.creatorSchulze, Felix
dc.creatorSimon, Miles
dc.date2007-06-04
dc.date.accessioned2026-07-07T08:04:03Z
dc.date.available2026-07-07T08:04:03Z
dc.descriptionWe study the Ricci flow for initial metrics which are C^0 small perturbations of the Euclidean metric on R^n. In the case that this metric is asymptotically Euclidean, we show that a Ricci harmonic map heat flow exists for all times, and converges uniformly to the Euclidean metric as time approaches infinity. In proving this stability result, we introduce a monotone integral quantity which measures the deviation of the evolving metric from the Euclidean metric. We also investigate the convergence of the diffeomorphisms relating Ricci harmonic map heat flow to Ricci flow.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/0706.0421
dc.identifierhttp://arxiv.org/abs/0706.0421
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129808
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53C44, 35B35
dc.titleStability of Euclidean space under Ricci flow
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