Advanced Studies in Pure Mathematics

A gap theorem for ancient solutions to the Ricci flow

Takumi Yokota

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543086335

Digital Object Identifier
doi:10.2969/aspm/05710505

Mathematical Reviews number (MathSciNet)
MR2648276

Zentralblatt MATH identifier
1197.53086

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

Keywords
Ricci flow reduced volume asymptotic volume ratio gradient Ricci soliton

Citation

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


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