Convex Functions and Spacetime Geometry

Abstract

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu })$ or an initial data set $(\Sigma ,h_{ij},K_{ij})$ admitting a suitably defined convex function. We show how the existence of a convex function on a spacetime places restrictions on the properties of the spacetime geometry.

26 pages, latex, 7 figures, improved version. some claims removed, references added

References in corpus (1)

• Cosmological spacetimes not covered by a constant mean curvature slicing

Cited by in corpus (2)

• Lorentzian Calderón problem under curvature bounds
• Space-time convex functions and sectional curvature