Type of finite time singularities of the Ricci flow with bounded scalar curvature

TL;DR

This paper investigates finite time singularities in Ricci flow on closed manifolds with bounded scalar curvature, characterizing the behavior of Type I singularities in dimensions 4 to 7.

Contribution

It establishes properties of blow-up sequences at finite time singularities for Ricci flows with bounded scalar curvature in specific dimensions.

Findings

Finite time singularities exhibit specific properties in dimensions 4 to 7.

Blow-up sequences of locally Type I singularities have certain defined characteristics.

Results extend understanding of singularity formation in Ricci flow with bounded scalar curvature.

Abstract

In this paper, we study the Ricci flow on a closed manifold of dimension $n \ge 4$ and finite time interval $[0,T)~(T < \infty)$ on which the scalar curvature are uniformly bounded. We prove that if such flow of dimension $4 \le n \le 7$ has finite time singularities, then every blow-up sequence of a locally Type I singularity has certain property. Here, locally Type I singularity is what Buzano and Di-Matteo defined.