2022/02/04 by Giuseppe Gentile, Gentile, Giuseppe, Boris Vertman +1
Mathematics · #53E10 #58J35 #83C05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2202.02424
openalex publication_date 2022/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider the prescribed mean curvature flow of a non-compact\nspace-like Cauchy hypersurface of bounded geometry in a generalized\nRobertson-Walker space-time. We prove that the flow preserves the\nspace-likeness condition and exists for infinite time. We also prove\nconvergence in the setting of manifolds with boundary. Our discussion\ngeneralizes previous work by Ecker, Huisken, Gerhardt and others with respect\nto a crucial aspects: we consider any non-compact Cauchy hypersurface under the\nassumption of bounded geometry. Moreover, we specialize the aforementioned\nworks by considering globally hyperbolic Lorentzian space-times equipped with a\nspecific class of warped product metrics.\n