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arXiv · 2510.14019

Diameter bounds in 3d Type I Ricci flows

Panagiotis Gianniotis
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Abstract

We prove that a three dimensional compact Ricci flow that encounters a Type I singularity has uniformly bounded diameter up to the singular time, thus giving an affirmative answer - for Type I singularities - to a conjecture of Perelman. To achieve this, we introduce a concept of a neck-region for a Ricci flow, analogous to the neck-regions introduced by Jiang-Naber and Cheeger-Jiang-Naber, in the study of Ricci limit spaces. We then prove that the associated packing measure is, in a certain sense, Ahlfors regular, a result that holds in any dimension.

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Panagiotis Gianniotis. 2025-10-15. Diameter bounds in 3d Type I Ricci flows. https://arxiv.org/abs/2510.14019

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