2022/11/21 by Luke T. Peachey, Peachey, Luke Thomas
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2211.11866
openalex publication_date 2022/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Ricci flow spacetimes were introduced by Kleiner & Lott as a way to describe Ricci flow through singularities, and have since been used elsewhere in the literature, prompting the question of their rigidity. In (2+1)-dimensions, we show that every complete and sufficiently regular spacetime must be a cylindrical spacetime. That is, if the metric is complete on each spatial slice, after imposing a necessary continuity condition, we can conclude that every spatial slice must be diffeomorphic to a fixed surface, and the Ricci flow spacetime is isometric to a classical Ricci flow on this surface.