Convergence of the Ricci flow toward a soliton

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Abstract

We will consider a τ-flow, given by the equation d/dtgij = -2Rij + 1/7tau;gij on a closed manifold M, for all times t ∈ [0, ∞). We will prove that if the curvature operator and the diameter of (M, g(t)) are uniformly bounded along the flow, then we have a sequential convergence of the flow toward the solitons. If we also assume that one of the limit solitons is integrable, then we have a convergence toward a unique soliton, up to a diffeomorphism.

Original languageEnglish (US)
Pages (from-to)283-343
Number of pages61
JournalCommunications in Analysis and Geometry
Volume14
Issue number2
DOIs
StatePublished - Mar 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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