Rotational symmetry of ancient solutions to the Ricci flow in dimension $3$ -- The compact case

S. Brendle

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arXiv · 1904.07835

Rotational symmetry of ancient solutions to the Ricci flow in dimension $3$ -- The compact case

S. Brendle

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Abstract

In [4], we proved that every noncompact ancient $\kappa$-solution to the Ricci flow in dimension $3$ is either locally isometric to a family of shrinking cylinders, or isometric to the Bryant soliton. In the same paper, we announced that the same method implies that compact ancient $\kappa$-solutions are rotationally symmetric. In this note we provide the details of this argument.

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S. Brendle. 2019-04-16. Rotational symmetry of ancient solutions to the Ricci flow in dimension $3$ -- The compact case. https://arxiv.org/abs/1904.07835

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