Calculus of Variations and Geometric Measure Theory

G. Di Matteo

Analysis of Type I Singularities in the Harmonic Ricci Flow

created by dimatteo on 01 Sep 2020



Inserted: 1 sep 2020
Last Updated: 1 sep 2020

Year: 2018

ArXiv: 1811.09563 PDF


In 2011 Enders, M\"{u}ller and Topping showed that any blow up sequence of a Type I Ricci flow near a singular point converges to a non-trivial gradient Ricci soliton, leading them to conclude that for such flows all reasonable definitions of singular points agree with each other. We prove the analogous result for the harmonic Ricci flow, generalizing in particular results of Guo, Huang and Phong and Shi. In order to obtain our result, we develop refined compactness theorems, a new pseudolocality theorem, and a notion of reduced length and volume based at the singular time for the harmonic Ricci flow.