Advanced Studies in Pure Mathematics

A gap theorem for ancient solutions to the Ricci flow

Takumi Yokota

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We outline the proof of the gap theorem stating that any ancient solution to the Ricci flow with Perelman's reduced volume whose asymptotic limit is sufficiently close to that of the Gaussian soliton must be isometric to the Euclidean space for all time. This is the main result of the author's paper [Yo].

Article information

Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 505-514

Received: 15 January 2009
Revised: 25 April 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document euclid.aspm/1543086335

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Ricci flow reduced volume asymptotic volume ratio gradient Ricci soliton


Yokota, Takumi. A gap theorem for ancient solutions to the Ricci flow. Probabilistic Approach to Geometry, 505--514, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710505.

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