arXiv research

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

Paper extends positive energy theorem to anti-de Sitter spacetimes.

We establish the inequality for Henneaux-Teitelboim's total energy-momentum for asymptotically anti-de Sitter initial data sets which are asymptotic to arbitrary $t$-slice in anti-de Sitter spacetime. In particular, when $t=0$, it generalizes Chruściel-Maerten-Tod's inequality in the center of AdS mass coordinates. We …

We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.

We define the total energy-momenta for (4+1)-dimensional asymptotically anti-de Sitter spacetimes, and prove the positive energy theorem for such spacetimes.

Study on constant mean curvature hypersurfaces in Anti-de Sitter space.

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

This paper proves a positive energy-momentum theorem for oriented Riemannian 3-manifolds that are asymptotic to a standard hyperbolic slice in anti de Sitter space-time. Analogously to the original Witten's proof in the asymptotically flat case, this result relies on spinorial methods. We also give a rigidity theorem: …

We prove existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces. Algebraically, these operators correspond to homomorphisms of generalized Verma modules. We relate these families to the asymp…

Study reveals how boundary wave operator determines metric properties on anti-de Sitter spacetimes.

We study geodesics along a noncompact Kerr-Newman instanton, where the asymptotic geometry is either de Sitter or anti-de Sitter. We use first integrals for the Hamilton-Jacobi equation to characterize trajectories both near and away from horizons. We study the interaction of geodesics with special features of the metr…

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

Research proves unique continuation for Einstein-vacuum equations on aAdS spacetimes.

We discuss several aspects of the relation between asymptotically AdS and asymptotically dS spacetimes including: the continuation between these types of spaces, the global stability of asymptotically dS spaces and the structure of limits within this class, holographic renormalization, and the maximal mass conjecture o…

Proof of Tholozan's volume formula for anti-de-Sitter 3-manifolds.

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

Study subelliptic heat kernel on octonionic anti-de Sitter space.

The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel of the fibration. The heat kernel formula is explicit enough to derive small time asymptotics. Related twistor spaces and corresponding heat kern…

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

Formulas derived for operators on forms in anti-de Sitter spaces.

Paper finds minimum volume for specific anti-de Sitter 3-manifolds.

Study classifies metrics on anti-de Sitter spacetime with specific symmetries.

Anti-de Sitter spacetimes with convex boundaries are uniquely determined by their boundary metrics.

We construct minimal surfaces in hyperbolic and anti-de Sitter 3-space with the topology of a $n$-punctured sphere by loop group factorization methods. The end behavior of the surfaces is based on the asymptotics of Delaunay-type surfaces, i.e., rotational symmetric minimal cylinders. The minimal surfaces in $\mathrm{H…

The paper connects Weil-Petersson homeomorphisms to maximal surfaces in anti-de Sitter space.

Solves Dirichlet problem for prescribed scalar curvature in Anti-de Sitter space

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

Study null surfaces of pseudo-spherical curves in anti-de Sitter space.

We establish a type of positive energy theorem for asymptotically anti-de Sitter Einstein-Maxwell initial data sets by using Witten's spinoral techniques.

Anti-de Sitter space is the Lorentzian space form with negative curvature. In this paper we consider lightlike hypersurfaces along spacelike submanifolds in anti-de Sitter space with general codimension. In particular, we investigate the singularities of lightlike hypersurfaces as an application of the theory of Legend…

Classification of specific pseudo-Riemannian manifolds.

It is shown that timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL(2,R) via Bryant type representation formulae. These formulae are used to investigate an explicit one-to-one correspondence, the s…

Study harmonic maps and anti-de Sitter 3-manifolds.

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

The paper classifies surfaces with constant curvature in 3D De Sitter and anti De Sitter spaces.

In this paper, we determine the type numbers of the pseudo-hyperbolic Gauss maps of all oriented Lorentzian surfaces of constant mean and Gaussian curvatures and non-diagonalizable shape operator in the $3$-dimensional anti-de Sitter space. Also, we investigate the behavior of type numbers of the pseudo-hyperbolic Gaus…

A geometrical correspondence between maximal surfaces in anti-De Sitter space-time and minimal surfaces in the Riemannian product of the hyperbolic plane and the real line is established. New examples of maximal surfaces in anti-De Sitter space-time are obtained in order to illustrate this correspondence.

Study on linear independence of Poincaré series for anti-de Sitter 3-manifolds.

In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally hyperbolic maximal Cauchy-compact anti-de Sitter manifolds in order to define an augmented moduli space. Moreover, we introduce a coordinate system in this space that resembles…

The paper proves a rigidity theorem for null geodesic travel times in asymptotically AdS spacetimes.

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…

We study spacelike hypersurfaces in anti-De Sitter spacetime that evolve by the Lagrangian angle of their Gauß maps.

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

The paper adapts metrics to anti-de Sitter structures, characterizing their degeneracies.

Anti-de Sitter spacetimes embed cone-metrics as bent Cauchy surfaces.

We prove that any weakly acausal curve $Γ$ in the boundary of Anti-de Sitter (2+1)-space is the asymptotic boundary of two spacelike $K$-surfaces, one of which is past-convex and the other future-convex, for every $K\in(-\infty,-1)$. The curve $Γ$ is the graph of a quasisymmetric homeomorphism of the circle if and only…

We study the subelliptic heat kernel of the sub-Laplacian on a 2n+1-dimensional anti-de Sitter space H2n+1 which also appears as a model space of a CR Sasakian manifold with constant negative sectional curvature. In particular we obtain an explicit and geometrically meaningful formula for the subelliptic heat kernel. T…

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