Ricci flow neckpinches without rotational symmetry

James Isenberg, Dan Knopf, Nataša Šešum

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We study “warped Berger” solutions (S1×S3, G(t)) of Ricci flow: generalized warped products with the metric induced on each fiber {s}×SU(2) a left-invariant Berger metric. We prove that this structure is preserved by the flow, that these solutions develop finite-time neckpinch singularities, and that they asymptotically approach round product metrics in space–time neighborhoods of their singular sets, in precise senses. These are the first examples of Ricci flow solutions without rotational symmetry that become asymptotically rotationally symmetric locally as they develop local finite-time singularities.

Original languageEnglish (US)
Pages (from-to)1860-1894
Number of pages35
JournalCommunications in Partial Differential Equations
Volume41
Issue number12
DOIs
StatePublished - Dec 1 2016

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Asymptotic symmetry formation
  • Ricci flow neckpinch
  • cohomogeneity-one metrics

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