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September 2020 Ancient solutions to the Ricci flow in dimension $3$
Simon Brendle
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Acta Math. 225(1): 1-102 (September 2020). DOI: 10.4310/ACTA.2020.v225.n1.a1

Abstract

It follows from work of Perelman that any finite-time singularity of the Ricci flow on a compact $3$-manifold is modeled on an ancient $\varkappa$-solution.

We prove that every non-compact ancient $\varkappa$-solution in dimension $3$ is isometric to a family of shrinking cylinders (or a quotient thereof), or to the Bryant soliton. This confirms a conjecture of Perelman.

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Simon Brendle. "Ancient solutions to the Ricci flow in dimension $3$." Acta Math. 225 (1) 1 - 102, September 2020. https://doi.org/10.4310/ACTA.2020.v225.n1.a1

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Received: 31 January 2019; Published: September 2020
First available in Project Euclid: 16 January 2021

Digital Object Identifier: 10.4310/ACTA.2020.v225.n1.a1

Rights: Copyright © 2020 Institut Mittag-Leffler

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Vol.225 • No. 1 • September 2020
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