Ricci flow on asymptotically conical surfaces with nontrivial topology

James Isenberg, Natasa Sesum, Rafe Mazzeo

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


As part of the general investigation of Ricci flow on complete surfaces with finite total curvature, we study this flow for surfaces with asymptotically conical (which includes as a special case asymptotically Euclidean) geometries. After establishing long-time existence, and in particular the fact that the flow preserves the asymptotically conic geometry, we prove that the solution metric g (t) expands at a locally uniform linear rate; moreover, the rescaled family of metrics t-1g(t) exhibits a transition at infinite time inasmuch as it converges locally uniformly to a complete, finite area hyperbolic metric which is the unique uniformizing metric in the conformal class of the initial metric g0.

Original languageEnglish (US)
Pages (from-to)227-248
Number of pages22
JournalJournal fur die Reine und Angewandte Mathematik
Issue number676
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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