2021/05/13 by Annalisa Cesaroni, Cesaroni, Annalisa, Heiko Kröner +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2105.06359
openalex publication_date 2021/05/13 · openalex created_date 2022/09/13 · openalex updated_date 2026/07/28
We consider the anisotropic mean curvature flow of entire Lipschitz graphs.\nWe prove existence and uniqueness of expanding self-similar solutions which are\nasymptotic to a prescribed cone, and we characterize the long time behavior of\nsolutions, after suitable rescaling, when the initial datum is a sublinear\nperturbation of a cone. In the case of regular anisotropies, we prove the\nstability of self-similar solutions asymptotic to strictly mean convex cones,\nwith respect to perturbations vanishing at infinity. We also show the stability\nof hyperplanes, with a proof which is novel also for the isotropic mean\ncurvature flow.\n