Athanase Papadopoulos

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We study the ideal triangulation graph T (S) of a punctured surface S of finite type. We show that if S is not the sphere with at most three punctures or the torus with one puncture, then the natural map from the extended mapping class group of S into the simplicial automorphism group of T (S) is an isomorphism. We also show that under the same conditions(More)
The space of broken hyperbolic structures generalizes the usual Teichmüller space of a punctured surface, and the space of projectivized broken measured foliations–or equivalently, the space of projectivized affine foliations of a punctured surface–likewise admits a generalization to projectivized broken measured foliations. Just as projectivized measured(More)
Let X be a CAT (−1)-space which is spherically symmetric around some point x0 ∈ X and whose boundary has finite positive s−dimensional Hausdorff measure. Let μ = (μx)x∈X be a conformal density of dimension d > s/2 on ∂X. We prove that μx0 is a weak limit of measures supported on spheres centered at x0. These measures are expressed in terms of the total mass(More)
A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. The aim of this paper is to present some interesting weak metrics and to study some of their properties. In particular, we introduce a weak metric, called the Apollonian weak metric, on any subset of a Euclidean space which is either(More)
We introduce Fenchel-Nielsen coordinates on Teichmüller spaces of surfaces of infinite type. The definition is relative to a given pair of pants decomposition of the surface. We start by establishing conditions under which any pair of pants decomposition on a hyperbolic surface of infinite type can be turned into a geometric decomposition, that is, a(More)
David Hilbert discovered in 1895 an important metric that is canonically associated to an arbitrary convex domain Ω in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof of this fact assumes a certain degree of smoothness of the boundary of Ω, and refers to a theorem by Busemann and Mayer that produces the norm(More)