On the equivalence between noncollapsing and bounded entropy for ancient solutions to the Ricci flow

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Abstract

As a continuation of a previous paper, we prove Perelman's assertion, that is, for ancient solutions to the Ricci flow with bounded nonnegative curvature operator, uniformly bounded entropy is equivalent to κ-noncollapsing on all scales. We also establish an equality between the asymptotic entropy and the asymptotic reduced volume, which is a result similar to a paper by Xu (2017), where he assumes the Type I curvature bound.

Original languageEnglish (US)
Pages (from-to)35-51
Number of pages17
JournalJournal fur die Reine und Angewandte Mathematik
Volume2020
Issue number762
DOIs
StatePublished - May 1 2020
Externally publishedYes

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