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arXiv · 1702.02652

Space-time convex functions and sectional curvature

Stephanie B. Alexander·William A. Karr
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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 Al\'ias, Bessa and deLira ruling out trapped submanifolds.

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Stephanie B. Alexander, William A. Karr. 2017-02-08. Space-time convex functions and sectional curvature. https://arxiv.org/abs/1702.02652

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