12 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Institut de Recherche Mathématique AvancéeFR147 papers
- Université de StrasbourgFR9 papers
- Institut national de recherche en sciences et technologies du numériqueFR8 papers
- Laboratoire Jacques-Louis LionsFR8 papers
- Centre National de la Recherche ScientifiqueFR7 papers
- Laboratoire Analyse, Géométrie et ApplicationsFR6 papers
- Laboratoire de Mathématiques Jean LerayFR5 papers
- Université de LorraineFR5 papers
- Université Paris CitéFR5 papers
- Institut Élie Cartan de LorraineFR4 papers
- Laboratoire de Mathématiques d'OrsayFR4 papers
- Laboratoire de Mathématiques Raphaël SalemFR4 papers
24 papers · 1 filter
The combinatorial structure of the unit tangent spheres and cotangent spheres of Teichm{ü}ller space with Thurston's Finsler metric
Ken'Ichi Ohshika, Athanase Papadopoulos
We prove several new results on the combinatorial structures of the unit spheres of the norms induced by Thurston's metric on the tangent and cotangent spaces of the Teichm{ü}ller…
Integrals of general geometric random variables on the moduli space of hyperbolic surfaces
Victor Le Guilloux
In this article we provide an integration formula enabling us to integrate random variables defined on the moduli space of hyperbolic surfaces which involve the lengths of closed g…
Notes on angles and solid angles, in relation with Euler's memoir De mensura angulorum solidorum
Stelios Negrepontis, Athanase Papadopoulos
We provide some historical context to the study of solid angles carried out by Euler in his memoir \emph{De mensura angulorum solidorum} (On the measure of solid angles). We extend…
Convex structures of the unit tangent spheres in Teichm{ü}ller space
Assaf Bar-Natan, Ken'Ichi Ohshika, Athanase Papadopoulos
We analyse the convex structure of the Finsler infinitesimal balls of the Thurston metric on Teichm{ü}ller space. We analyse the convex structure of the Finsler unit ball in the ta…
The earthquake metric on Teichm{ü}ller space
Yi Huang, Ken'ichi Ohshika, Huiping Pan +1
This is the first paper to systematically study the earthquake metric, an asymmetric Finsler metric on Teichm{ü}ller space introduced by Thurston. We provide proofs for several ass…
The infinitesimal and global Thurston geometry of Teichm{ü}ller space
Yi Huang, Ken'Ichi Ohshika, Athanase Papadopoulos
We undertake a systematic study of the infinitesimal geometry of the Thurston metric, showing that the topology, convex geometry and metric geometry of the tangent and cotangent sp…
Minimal stretch maps between Euclidean triangle?
Ismail Saglam, Athanase Papadopoulos
Given two triangles whose angles are all acute, we find a homeomorphism with the smallest Lipschitz constant between them and we give a formula for the Lipschitz constant of this m…
Ideal triangles, hyperbolic surfaces and the Thurston metric on Teichm{ü}ller space
Athanase Papadopoulos
These are notes on the hyperbolic geometry of surfaces, Teichm{ü}ller spaces and Thurston's metric on these spaces. They are associated with lectures I gave at the Morningside Cent…
W. P. Thurston and French mathematics
François Laudenbach, Athanase Papadopoulos
We give a general overview of the influence of William Thurston on the French mathematical school and we show how some of the major problems he solved are rooted in the French math…
Bijections of geodesic lamination space preserving left Hausdorff convergence
Ken'Ichi Ohshika, Athanase Papadopoulos
We introduce an asymmetric distance function, which we call the `left Hausdorff distance function', on the space of geodesic laminations on a closed hyperbolic surface of genus at…
Homeomorphisms and intersection number
Ken'Ichi Ohshika, Athanase Papadopoulos
We prove two rigidity results for automorphism groups of the spaces ML(S) of measured laminations on a closed hyperbolic surface S and PML(S) of projective measured laminations on…
Transitional geometry
Athanase Papadopoulos, Norbert A'Campo
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geom…
Actions of mapping class groups
Athanase Papadopoulos
This paper has three parts. The first part is a general introduction to rigidity and to rigid actions of mapping class group actions on various spaces. In the second part, we descr…
Convex real projective structures and Hilbert metrics
Inkang Kim, Athanase Papadopoulos
We review some basic concepts related to convex real projective structures from the differential geometry point of view. We start by recalling a Riemannian metric which originates…
Thurston's metric on Teichmüller space and isomorphisms between Fuchsian groups
Athanase Papadopoulos, Weixu Su
The aim of this paper is to relate Thurston's metric on Teichmüller space to several ideas initiated by T. Sorvali on isomorphisms between Fuchsian groups. In particular, this will…
The Funk and Hilbert geometries for spaces of constant curvature
Athanase Papadopoulos, Sumio Yamada
The goal of this paper is to introduce and study analogues of the Euclidean Funk and Hilbert metrics on open convex subsets of hyperbolic or spherical spaces. At least at a for…
On the coarse geometry of the complex of domains
Valentina Disarlo
The complex of domains is a geometric tool with a very rich simplicial structure, it contains the curve complex as a simplicial subcomplex. In this paper we shall reg…
On the ideal triangulation graph of a punctured surface
Mustafa Korkmaz, Athanase Papadopoulos
We study the ideal triangulation graph of a punctured surface of finite type. We show that if is not the sphere with at most three punctures or the torus with one pu…
Shortening all the simple closed geodesics on surfaces with boundary
Athanase Papadopoulos, Guillaume Théret
We give a proof of an unpublished result of Thurston showing that given any hyperbolic metric on a surface of finite type with nonempty boundary, there exists another hyperbolic me…
Length spectra and the Teichmueller metric for surfaces with boundary
Lixin Liu, Athanase Papadopoulos, Weixu Su +1
We consider some metrics and weak metrics defined on the Teichmueller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectru…
On length spectrum metrics and weak metrics on Teichmueller spaces of surfaces with boundary
Lixin Liu, Athanase Papadopoulos, Weixu Su +1
We define and study metrics and weak metrics on the Teichmueller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the…
Some metrics on Teichmüller spaces of surfaces of infinite type
Lixin Liu, Athanase Papadopoulos
Unlike the case of surfaces of topologically finite type, there are several different Teichmüller spaces that are associated to a surface of topological infinite type. These Teichm…
A rigidity theorem for the mapping class group action on the space of unmeasured foliations on a surface
Athanase Papadopoulos
Let be a surface of finite type which is not a sphere with at most four punctures, a torus with at most two punctures, or a closed surface of genus two. Let be t…
Well displacing representations and orbit maps
Thomas Delzant, Olivier Guichard, François Labourie +1
We discuss in this article a property of action of groups by isometries called "well displacing". An action is said to be well displacing, if the displacement function is equivalen…