An $\epsilon$-Regularity Theorem for Non-collapsed Ricci Flow

Harry Fluck; Max Hallgren

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arXiv · 2509.14154

An $\epsilon$-Regularity Theorem for Non-collapsed Ricci Flow

Harry Fluck·Max Hallgren

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Abstract

In this article we prove an $\epsilon$-regularity theorem for non-collapsed Ricci flows, and use this to prove new estimates for singularity models of Fano K\"ahler-Ricci flows. In the course of our proof, we find a criterion for uniform convergence of solutions to the heat equation along a sequence of $\mathbb{F}$-converging Ricci flows, and apply this to new parabolic regularizations of some natural geometric quantities.

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Harry Fluck, Max Hallgren. 2025-09-17. An $\epsilon$-Regularity Theorem for Non-collapsed Ricci Flow. https://arxiv.org/abs/2509.14154

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