Il giorno mercoledì 22 Novembre alle ore 14:00 in aula 3014 François Fillastre (Université de Montpellier) terrà il seguente seminario:
Title: Embedding of flat metrics on compact surfaces in flat (2+1) spacetimes
Abstract: Joint work with Roman Prosanov (TU Vienna).
We first prove that, given a flat metric d on a compact surface S with negative singular curvatures, given a hyperbolic metric h on S, we can isometrically embed d as a convex polyhedral surface in a (essentially unique) flat globally hyperbolic (GH) spacetime with linear part of the holonomy given by h.
This statement has a purely two dimensional version, involving balanced geodesic cellulations over (S,h). These objects are the discrete analogues of 1-harmonic maps introduced by Trapani and Valli, or equivalently, of Codazzi tensors. They are also an analogue of measured geodesic laminations.
We then state a simultaneous uniformization theorem, saying that any pair of flats metrics on S defines a flat GH spacetime. The proof is by minimization of a functional over balanced geodesic cellulations, which is the analogue of the total length in the case of measured lamination (Bonahon), or of the "(1,0)-energy'' in the case of Codazzi tensors (Smith).
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