The size of the singular set of a Type I Ricci flow

TL;DR

This paper studies the structure of singularities in Type I Ricci flows by stratifying the blow-up set and relating it to volume decay rates, providing a geometric dimension estimate of the singular set.

Contribution

It introduces a stratification of the singular set based on tangent flow Euclidean factors and links these strata to volume decay rates, offering new insights into the singular set's size.

Findings

Stratification of the singular set according to Euclidean factors.

Characterization of strata via volume decay rates.

Dimension estimates for the singular set.

Abstract

In a singular Type I Ricci flow, we consider a stratification of the set where there is curvature blow-up, according to the number of the Euclidean factors split by the tangent flows. We then show that the strata are characterized roughly in terms of the decay rate of their volume, which in our context plays the role of a dimension estimate.