An $\epsilon$-regularity theorem for Perelman's reduced volume

Liang Cheng; Yongjia Zhang

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arXiv · 2502.15219

An $\epsilon$-regularity theorem for Perelman's reduced volume

Liang Cheng·Yongjia Zhang

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Abstract

In this article, we prove an $\epsilon$-regularity theorem for Perelman's reduced volume. We show that on a Ricci flow, if Perelman's reduced volume is close to $1$, then the curvature radius at the base point cannot be too small.

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Liang Cheng, Yongjia Zhang. 2025-02-21. An $\epsilon$-regularity theorem for Perelman's reduced volume. https://arxiv.org/abs/2502.15219

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