73 citations · 122 across the 8 of their papers we have counts for
8 papers
Polyhedral surfaces in flat (2+1)-spacetimes and balanced cellulations on hyperbolic surfaces
François Fillastre, Roman Prosanov
We first prove that given a hyperbolic metric on a closed surface , any flat metric on with negative singular curvatures isometrically embeds as a convex polyhedral Cauc…
Measuring Fermionic Entanglement: Entropy, Negativity, and Spin Structure
Eyal Cornfeld, Eran Sela, Moshe Goldstein
The recent direct experimental measurement of quantum entanglement paves the way towards a better understanding of many-body quantum systems and their correlations. Nevertheless, t…
Embeddings of non-positively curved compact surfaces in flat Lorentzian manifolds
François Fillastre, Dmitriy Slutskiy
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 spac…
Hyperbolization of cusps with convex boundary
François Fillastre, Ivan Izmestiev, Giona Veronelli
We prove that for every metric on the torus with curvature bounded from below by -1 in the sense of Alexandrov there exists a hyperbolic cusp with convex boundary such that the ind…
Shapes of polyhedra, mixed volumes, and hyperbolic geometry
Francois Fillastre, Ivan Izmestiev
We are generalizing to higher dimensions the Bavard-Ghys construction of the hyperbolic metric on the space of polygons with fixed directions of edges. The space of convex d-dimens…
Fuchsian convex bodies: basics of Brunn--Minkowski theory
Francois Fillastre
The hyperbolic space $ \H^d$ can be defined as a pseudo-sphere in the Minkowski space-time. In this paper, a Fuchsian group is a group of linear isometries of the Minko…
Flippable tilings of constant curvature surfaces
Francois Fillastre, Jean-Marc Schlenker
We call "flippable tilings" of a constant curvature surface a tiling by "black" and "white" faces, so that each edge is adjacent to two black and two white faces (one of each on ea…
From spaces of polygons to spaces of polyhedra following Bavard, Ghys and Thurston
Francois Fillastre
After work of W. P. Thurston, C. Bavard and É. Ghys constructed particular hyperbolic polyhedra from spaces of deformations of Euclidean polygons. We present this construction as a…