The rigidity of S3 × R under ancient Ricci flow

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Abstract

In this paper we generalize the neck-stability theorem of Kleiner-Lott [8] to a special class of four-dimensional nonnegatively curved Type I κ-solutions, namely, those whose asymptotic shrinkers are the standard cylinder S3 × R. We use this stability result to prove a rigidity theorem: if a four-dimensional Type I κ-solution with nonnegative curvature operator has the standard cylinder S3 × R as its asymptotic shrinker, then it is exactly the cylinder with its standard shrinking metric.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Aug 17 2017
Externally publishedYes

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