Embeddings of non-positively curved compact surfaces in flat Lorentzian manifolds

2017/03/21 by Fillastre, François, Slutskiy, Dmitriy
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.07253

Abstract

We prove that any metric of non-positive curvature in the sense of Alexandrov on a compact surface can be isometrically embedded as a convex spacelike Cauchy surface in a flat spacetime of dimension (2+1). The proof follows from polyhedral approximation.

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