Francesco Bonsante

Collisions of Particles in Locally AdS Spacetimes I. Local Description and Global Examples

We investigate 3-dimensional globally hyperbolic AdS manifolds (or more generally constant curvature Lorentz manifolds) containing “particles”, i.e., cone singularities along a graph Γ. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than 2π on time-like singular segments). We construct examples of such manifolds, describe the cone singularities that can arise and the way they can interact (the local geometry near the vertices of Γ). We then adapt to this setting some notions like global hyperbolicity which are natural for Lorentz manifolds, and construct some examples of globally hyperbolic AdS manifolds with interacting particles.

Fixed points of compositions of earthquakes

Let S be a closed surface of genus at least 2, and consider two measured geodesic laminations that fill S. Right earthquakes along these laminations are diffeomorphisms of the Teichmuller space of S. We prove that the composition of these earthquakes has a fixed point in the Teichmuller space. Another way to state this result is that it is possible to prescribe any two measured laminations that fill a surface as the upper and lower measured bending laminations of the convex core of a globally hyperbolic AdS manifold. The proof uses some estimates from the geometry of those AdS manifolds.

A cyclic extension of the earthquake flow I

The landslide flow, introduced in (5), is a smoother analog of the earthquake flow on Teichmuller space which shares some of its key properties. We show here that further properties of earthquakes apply to landslides. The landslide flow is the Hamiltonian flow of a convex function. The smooth grafting map sgr taking values in Teichmuller space, which is to landslides as grafting is to earthquakes, is proper and surjective with respect to either of its variables. The smooth grafting map SGr taking values in the space of complex projective structures is symplectic (up to a multiplicative constant). The composition of two landslides has a fixed point on Teichmuller space. As a consequence we obtain new results on constant Gauss curvature surfaces in 3-dimensional hyperbolic or AdS manifolds. We also show that the landslide flow has a satisfactory extension to the boundary of Teichmuller space.

Area‐preserving diffeomorphisms of the hyperbolic plane and K‐surfaces in anti‐de Sitter space

We prove that any weakly acausal curve

Canonical Wick rotations in 3-dimensional gravity

\Gamma

Flat spacetimes with compact hyperbolic Cauchy surfaces

in the boundary of Anti-de Sitter (2+1)-space is the asymptotic boundary of two spacelike

Ads Manifolds With Particles and Earthquakes on Singular Surfaces

K

Maximal surfaces and the universal Teichmüller space

-surfaces, one of which is past-convex and the other future-convex, for every

Multi-black Holes and Earthquakes on Riemann Surfaces with Boundaries

K\in(-\infty,-1)

Some open questions on anti-de Sitter geometry

. The curve