Space-time convex functions and sectional curvature

Original · EN

We show that in Lorentzian manifolds, sectional curvature bounds of the form R≤ K, as defined by Andersson and Howard, are closely tied to space-time convex and λ-convex (λ>0) functions, as defined by Gibbons and Ishibashi. Among the consequences are a natural construction of such functions, and an analogue, that applies to domains of a new type, of a theorem of Alías, Bessa and deLira ruling out trapped submanifolds.