Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature

Bennett Chow, David Glickenstein, Peng Lu

Research output: Contribution to journalReview article

5 Scopus citations

Abstract

We study sequences of 3-dimensional solutions to the Ricci flow with almost nonnegative sectional curvatures and diameters tending to infinity. Such sequences may arise from the limits of dilations about singularities of Type IIb. In particular, we study the case when the sequence collapses, which may occur when dilating about infinite time singularities. In this case we classify the possible Gromov-Hausdorff limits and construct 2-dimensional virtual limits. The virtual limits are constructed using Fukaya theory of the limits of local covers. We then show that the virtual limit arising from appropriate dilations of a Type IIb singularity is always Hamilton's cigar soliton solution.

Original languageEnglish (US)
Pages (from-to)1-28
Number of pages28
JournalMathematische Zeitschrift
Volume254
Issue number1
DOIs
StatePublished - Sep 1 2006

ASJC Scopus subject areas

  • Mathematics(all)

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