Constant mean curvature foliations of simplicial flat spacetimes

Original · EN

Benedetti and Guadagnini have conjectured that the marked lenght spectrum of the constant mean curvature foliation Mτ in a 2+1 dimensional flat spacetime V with compact hyperbolic Cauchy surfaces converges, in the direction of the singularity, to that of the marked measure spectrum of the R-tree dual to the measured foliation corresponding to the translational part of the holonomy of V. We prove that this is the case for n+1 dimensional, n ≥ 2, simplicial flat spacetimes with compact hyperbolic Cauchy surface. A simplicial spacetime is obtained from the Lorentz cone over a hyperbolic manifold by deformations corresponding to a simple measured foliation.