2022/12/15 by Salvatore Stuvard, Yoshihiro Tonegawa, Stuvard, Salvatore +1 · 1 citation
Mathematics · Physics and Astronomy · #35B65 #49Q15 #53E10 #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2212.07727
openalex publication_date 2022/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a general k-dimensional Brakke flow in ℝn locally close to a k-dimensional plane in the sense of measure, it is proved that the flow is represented locally as a smooth graph over the plane with estimates on all the derivatives up to the end-time. Moreover, at any point in space-time where the Gaussian density is close to 1, the flow can be extended smoothly as a mean curvature flow up to that time in a neighborhood: this extends White's local regularity theorem to general Brakke flows. The regularity result is in fact obtained for more general Brakke-like flows, driven by the mean curvature plus an additional forcing term in a dimensionally sharp integrability class or in a Hölder class.