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arXiv · 1803.03660

A note on Perelman's no shrinking breather theorem

Yongjia Zhang
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Abstract

As an application of his entropy formula, Perelman proved that every compact shrinking breather is a shrinking gradient Ricci soliton. We give a proof for the complete noncompact case by using Perelman's $\mathcal{L}$-geometry. Our proof follows the argument in Lu and Zheng of constructing an ancient solution, and removes a technical assumption made by them.

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Yongjia Zhang. 2018-03-09. A note on Perelman's no shrinking breather theorem. https://arxiv.org/abs/1803.03660

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