Space-time convex functions and sectional curvature

Abstract

We show that in Lorentzian manifolds, sectional curvature bounds of the form $\mathcal{R}\le K$, as defined by Andersson and Howard, are closely tied to space-time convex and $\lambda$-convex ($\lambda >0$) 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.

11 pages

References in corpus (1)

• Semiconcave functions in Alexandrov's geometry