Singular Ricci flows I

Bruce Kleiner, John Lott

Research output: Contribution to journalArticlepeer-review


We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. These provide a solution to the long-standing problem of finding a good notion of Ricci flow through singularities, in the 3-dimensional case. We prove that Ricci flow with surgery, starting from a fixed initial condition, subconverges to a singular Ricci flow as the surgery parameter tends to zero. We establish a number of geometric and analytical properties of singular Ricci flows.

Original languageEnglish (US)
Pages (from-to)65-134
Number of pages70
JournalActa Mathematica
Issue number1
StatePublished - Sep 2017

ASJC Scopus subject areas

  • General Mathematics


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