Convergence of the Ricci flow toward a soliton

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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
Issue number2
StatePublished - Mar 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


Dive into the research topics of 'Convergence of the Ricci flow toward a soliton'. Together they form a unique fingerprint.

Cite this