Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 505 - 514
A gap theorem for ancient solutions to the Ricci flow
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].
Received: 15 January 2009
Revised: 25 April 2009
First available in Project Euclid: 24 November 2018
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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. https://projecteuclid.org/euclid.aspm/1543086335