Almost splitting and quantitative stratification for super Ricci flow

TL;DR

This paper investigates the near-rigidity and structural properties of super Ricci flows with non-negative Muller quantity, extending Bamler's results and introducing new insights into scalar curvature behavior at almost selfsimilar points.

Contribution

It extends almost splitting and stratification theorems to super Ricci flows and introduces a novel almost constancy result for scalar curvature at selfsimilar points.

Findings

Established almost splitting and stratification theorems for super Ricci flow.

Proved an almost constancy property for scalar curvature at almost selfsimilar points.

Extended Bamler's results from Ricci flow to super Ricci flow.

Abstract

The aim of this paper is to study almost rigidity properties of super Ricci flow whose Muller quantity is non-negative. We conclude almost splitting and quantitative stratification theorems that have been established by Bamler for Ricci flow. As a byproduct, we obtain an almost constancy for a certain integral quantity concerning scalar curvature at an almost selfsimilar point, which is new even for Ricci flow.