On Ricci flows with closed and smooth tangent flows (Q6574283)

The authors consider Ricci flows admitting closed and smooth tangent flows in the sense of \textit{R. H. Bamler} [``Structure theory of non-collapsed limits of Ricci flows'', Preprint, \url{arXiv:2009.03243}]. A tangent flow of this type can be either a tangent flow at infinity for an ancient Ricci flow, or a tangent flow at a singular point for a Ricci flow developing a finite-time singularity. \N\NTheir main results are as follows: \N(a) In the considered relevant cases the tangent flow is unique; \N(b) If a Ricci flow with finite-time singularity has a closed singularity model, then the singularity is of Type I and the singularity model is the tangent flow at the singular point (thus answering a question posed in [\textit{B. Chow} et al., The Ricci flow: techniques and applications. Part III: Geometric-analytic aspects. Providence, RI: American Mathematical Society (AMS) (2010; Zbl 1216.53057)]); \N(c) A dichotomy theorem that characterizes ancient Ricci flows admitting a closed and smooth backward sequential limit.