Perelman's reduced volume and a gap theorem for the Ricci flow

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31 Citations (Scopus)


In this paper, we show that any ancient solution to the Ricci flow with the reduced volume whose asymptotic limit is sufficiently close to that of the Gaussian soliton is isometric to the Euclidean space for all time. This is a generalization of Anderson's result for Ricciflat manifolds. As a corollary, a gap theorem for gradient shrinking Ricci solitons is also obtained.

Original languageEnglish
Pages (from-to)227-263
Number of pages37
JournalCommunications in Analysis and Geometry
Issue number2
Publication statusPublished - 2009 Mar


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