Space-Time Convex Functions and Sectional Curvature

Abstract

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.