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

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

2008-08-03

arxiv.org/abs/0808.0303v3

Comm. Anal. Geom. 17 (2009), no. 2, 227--263

Mathematics

Differential Geometry

final version

Scientific paper

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 Ricci-flat manifolds. As a corollary, a
gap theorem for gradient shrinking Ricci solitons is also obtained.

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