Type of finite time singularities of the 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.

17 pages. arXiv admin note: text overlap with arXiv:2006.16227 by other authors

References in corpus (3)

• Structure theory of non-collapsed limits of Ricci flows
• Remarks on the extension of the Ricci flow
• A Local Singularity Analysis for the Ricci Flow and its Applications to Ricci Flows with Bounded Scalar Curvature