arXiv research

Link between Teichmüller and anti de Sitter geometry via length functions.

Study domination between non-Fuchsian surface group representations and anti-de Sitter geometry.

Combines non-Euclidean and de Sitter geometries on the plane.

Study on compact biconservative hypersurfaces in de Sitter space.

Study finds necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.

Study geodesics on Kerr-Newman instantons with de Sitter or anti-de Sitter asymptotics.

Introduces Anti-de Sitter geometry and its connection to Teichmüller theory.

Study on eigenvalues of Laplacian on anti-de Sitter manifolds.

Study $b$-$6j$ symbols linking anti-de Sitter tetrahedra to hyperbolic geometry.

In this paper, we generalize the defining equation for de Sitter space by replacing the de Sitter radius with a function $f$ satisfying certain conditions; each resulting hypersurface is diffeomorphic to de Sitter space, and has a geometry (and causal character) which is controlled by the choice of $f$. Necessary and s…

Proof of Thurston's earthquake theorem using Anti-de Sitter geometry.

In this paper we describe trigonometry on the de Sitter surface. For that a characterization of geodesics is given, leading to various types of triangles. We define lengths and angles of these. Then, transferring the concept of polar triangles from spherical geometry into the Minkowski space, we relate hyperbolic with …

No de Sitter black rings with ring topology exist.

Paper constructs geometric transitions between hyperbolic and Anti-de Sitter geometries.

Study dualities of geometric invariants on cuspidal edges in hyperbolic and de Sitter spaces.

The paper classifies space-like hypersurfaces with parallel Blaschke tensors in de Sitter space.

Study of 2D Lorentzian anti-de Sitter plane using geometric control theory.

Paper proves a Minkowski-like inequality in de Sitter space.

Integrable flows on null curves in anti-de Sitter 3-space studied.

Study the heat kernel on quaternionic anti-de Sitter spaces and related spaces.

Study para-hyperKähler geometry of anti-de Sitter structures.

It is proved that the geometry of lightlike hypersurfaces of the de Sitter space S^{n+1}_1 is directly connected with the geometry of hypersurfaces of the conformal space C^n. This connection is applied for a construction of an invariant normalization and an invariant affine connection of lightlike hypersurfaces as wel…

Sub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. The simplest example of sub-Riemannian structure is provided by the 3-D Heisenberg group. Sub-Riemannian Geometry enjoys major differences from the Riemannian being a generalisation of the la…

Crooked planes were defined by Drumm to bound fundamental polyhedra in Minkowski space for Margulis spacetimes. They were extended by Frances to closed polyhedral surfaces in the conformal compactification of Minkowski space (Einstein space) which we call crooked surfaces. The conformal model of anti-de Sitter space is…

Fixed points found in Teichmüller space via anti-de Sitter geometry.

The authors study singular points of lightlike hypersurfaces of the de Sitter space S^{n+1}_1 and the geometry of hypersurfaces and use them for construction of an invariant normalization and an invariant affine connection of lightlike hypersurfaces.

Uniqueness theorem for extremal charged black holes in de Sitter space.

New theorem proves uniqueness of Schwarzschild-de Sitter spacetime.

The study calculates the index distribution of Brownian loops in various geometrical settings.

The paper generalizes metrics on hyperbolic and anti-de Sitter spaces with curved boundaries.

Study on width of Jordan curves in complex projective space, distinguishing quasicircles.

Study equivariant embeddings into Anti-de Sitter space and their relation to Lagrangian submanifolds.

We find the minimal value of the length in de Sitter space of closed space-like curves with non-vanishing non-space-like geodesic curvature vector. These curves are in correspondence with closed almost-regular canal surfaces, and their length is a natural magnitude in conformal geometry. As an application, we get a low…

In a recent paper, Q. Mérigot proved that representations in SO(2,n) of uniform lattices of SO(1,n) which are Anosov in the sense of Labourie are quasi-Fuchsian, i.e. are faithfull, discrete, and preserve an acausal subset in the boundary of anti-de Sitter space. In the present paper, we prove the reverse implication. …

Study character varieties of a Coxeter group in hyperbolic and Anti-de Sitter spaces.

Study curves in a spacelike hypersurface using geometric and singularity theory.

Proves uniqueness of certain spacetime solutions with extremal horizons.

Study Lorentz harmonic maps and spacelike surfaces in anti-de Sitter space.

We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path i…

We study grassmannians associated with a linear space with a nondegenerate hermitian form. The geometry of these grassmannians allows us to explain the relation between a (pseudo-)riemannian projective geometry and the conformal structure on its ideal boundary (absolute). Such relation encompasses, for instance, the us…

Study of longest arcs and cut loci in deformed anti de-Sitter spaces.

This paper is devoted to a coordinate-free approach to several classic geometries such as hyperbolic (real, complex, quaternionic), elliptic (spherical, Fubini-Study), and lorentzian (de Sitter, anti de Sitter) ones. These geometries carry a certain simple structure that is in some sense stronger than the riemannian st…

Classification of specific pseudo-Riemannian manifolds.

De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates respectively. Two positive energy theorems were proved previously for certain $¶$-asymptotically de Sitter and $\H$-asymptotically de Sitter initial…

Proves optimal isoperimetric inequality in de Sitter space.

Study examines solutions to Jang equation on anti-de Sitter spacetimes.

Constructs many black hole spacetimes in de Sitter space.

Study lightlike hypersurfaces in anti-de Sitter space.