Connectivity by geodesics on a class of globally hyperbolic spacetimes

Abstract

During the past years there has been a considerable amount of research related to the problem of geodesic connectedness of Lorentzian manifolds. This topic has wide applications in Physics, but for mathematicians its interest is essentially due to the peculiar di culty of this natural problem, which makes it challenging from both an analytical and a geometrical point of view. In this talk I discuss the geodesic connectedness problem on globally hyper- bolic spacetimes endowed with a complete, timelike or lightlike, Killing vector eld and a complete Cauchy hypersurface. Then I introduce the notion of open subset with convex boundary and present some applications of previous results.