94 citations · 605 across the 65 of their papers we have counts for
36 papers · 1 filter
Gromov-Thurston manifolds and anti-de Sitter geometry
Daniel Monclair, Jean-Marc Schlenker, Nicolas Tholozan
We consider hyperbolic and anti-de Sitter (AdS) structures on , where is a -dimensional Gromov-Thurston manifold. If has cone angles greater than , we…
The geometric data on the boundary of convex subsets of hyperbolic manifolds
Qiyu Chen, Jean-Marc Schlenker
Let be a geodesically convex subset in a convex co-compact hyperbolic manifold with incompressible boundary. We assume that each boundary component of is either a bound…
The Weyl problem for unbounded convex domains in $\HH^3$
Jean-Marc Schlenker
Let $K\subset \HH^3$ be a convex subset in $\HH^3$ with smooth, strictly convex boundary. The induced metric on then has curvature . It was proved by Alexandrov…
On the Weyl problem for complete surfaces in the hyperbolic and anti-de Sitter spaces
Jean-Marc Schlenker
The classical Weyl problem (solved by Lewy, Alexandrov, Pogorelov, and others) asks whether any metric of curvature on the sphere is induced on the boundary of a unique c…
Minimizing immersions of a hyperbolic surface in a hyperbolic -manifold
Francesco Bonsante, Gabriele Mondello, Jean-Marc Schlenker
Let be a closed hyperbolic surface and be a quasi-Fuchsian 3-manifold. We consider incompressible maps from to that are critical points of an energy functional…
Hyperideal polyhedra in the 3-dimensional anti-de Sitter space
Qiyu Chen, Jean-Marc Schlenker
We study hyperideal polyhedra in the 3-dimensional anti-de Sitter space , which are defined as the intersection of the projective model of with a convex polyhedron i…
Hyperbolic ends with particles and grafting on singular surfaces
Qiyu Chen, Jean-Marc Schlenker
We prove that any hyperbolic end with particles (cone singularities along infinite curves of angles less than ) admits a unique foliation by constant Gauss curvature surfaces. U…
Constant Gauss curvature foliations of AdS spacetimes with particles
Qiyu Chen, Jean-Marc Schlenker
We prove that for any convex globally hyperbolic maximal (GHM) anti-de Sitter (AdS) 3-dimensional space-time with particles (cone singularities of angles less than along ti…
Symplectic Wick rotations between moduli spaces of 3-manifolds
Carlos Scarinci, Jean-Marc Schlenker
Given a closed hyperbolic surface , let $\cQF$ denote the space of quasifuchsian hyperbolic metrics on and $\cGH_{-1}$ the space of maximal globally hyperbolic anti-…
Polyhedra inscribed in a quadric
Jeffrey Danciger, Sara Maloni, Jean-Marc Schlenker
We study convex polyhedra in three-space that are inscribed in a quadric surface. Up to projective transformations, there are three such surfaces: the sphere, the hyperboloid, and…
The renormalized volume and uniformisation of conformal structures
Colin Guillarmou, Sergiu Moroianu, Jean-Marc Schlenker
We study the renormalized volume of asymptotically hyperbolic Einstein (AHE in short) manifolds when the conformal boundary $\pl M$ has dimension even. Its definition d…
Some open questions on anti-de Sitter geometry
Thierry Barbot, Francesco Bonsante, Jeffrey Danciger +6
We present a list of open questions on various aspects of AdS geometry, that is, the geometry of Lorentz spaces of constant curvature -1. When possible we point out relations with…
Collisions of particles in locally AdS spacetimes II Moduli of globally hyperbolic spaces
Thierry Barbot, Francesco Bonsante, Jean-Marc Schlenker
We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than along a time-like graph . To each such s…
The renormalized volume and the volume of the convex core of quasifuchsian manifolds
Jean-Marc Schlenker
We show that the renormalized volume of a quasifuchsian hyperbolic 3-manifold is equal, up to an additive constant, to the volume of its convex core. We also provide a precise uppe…
Non-rigidity of spherical inversive distance circle packings
Jiming Ma, Jean-Marc Schlenker
We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.
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…
Collisions of particles in locally AdS spacetimes I. Local description and global examples
Thierry Barbot, Francesco Bonsante, Jean-Marc Schlenker
We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph . We impose physically relevant conditions on the c…
Maximal surfaces and the universal Teichmüller space
Francesco Bonsante, Jean-Marc Schlenker
We show that any element of the universal Teichmüller space is realized by a unique minimal Lagrangian diffeomorphism from the hyperbolic plane to itself. The proof uses maximal su…
Profiles of inflated surfaces
Igor Pak, Jean-Marc Schlenker
We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more ge…
The Weil-Petersson metric and the renormalized volume of hyperbolic 3-manifolds
Kirill Krasnov, Jean-Marc Schlenker
We survey the renormalized volume of hyperbolic 3-manifolds, as a tool for Teichmuller theory, using simple differential geometry arguments to recover results sometimes first achie…
Collisions of particles in locally AdS spacetimes
Thierry Barbot, Francesco Bonsante, Jean-Marc Schlenker
We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph . We impose physically relevant conditions on the c…
A symplectic map between hyperbolic and complex Teichmüller theory
Kirill Krasnov, Jean-Marc Schlenker
Let be a closed, orientable surface of genus at least 2. The cotangent bundle of the "hyperbolic'' Teichmüller space of can be identified with the space $\CP$ of complex pr…
On the infinitesimal rigidity of polyhedra with vertices in convex position
Ivan Izmestiev, Jean-Marc Schlenker
Let be a polyhedron. It was conjectured that if is weakly convex (i. e. its vertices lie on the boundary of a strictly convex domain) and decomposable (i. e. $…
Notes on a paper of Mess
Lars Andersson, Thierry Barbot, Riccardo Benedetti +5
These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear…