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

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.

Publication Details

Journal
ArXiv.org
Published
2025-02-21
Primary Topic
Geometric Analysis and Curvature Flows
Type
article
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article

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

ArXiv.org
Geometric Analysis and Curvature Flows
article

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

article en

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.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 40%
Geometric Analysis and Curvature Flows
Open Access PDFOpenAlex
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An $\epsilon$-regularity theorem for Perelman's reduced volume · ArXiv.org (2025) | TGRS Research Map | TGRS