Study examines solutions to Jang equation on anti-de Sitter spacetimes.
problem Existence and properties of solutions to the generalized Jang equation.
method Rigorous analysis in asymptotically anti-de Sitter setting.
result Provides solutions for a broad class of asymptotic conditions.
We show that a stationary solution of the Einstein-Maxwell equations which is close to a non-degenerate Reissner-Nordström-de Sitter solution is in fact equal to a slowly rotating Kerr-Newman-de Sitter solution. The proof uses the non-linear stability of the Kerr-Newman-de Sitter family of black holes for small angular…
Classical 10d string backgrounds with a 4d de Sitter space-time, D-brane and orientifold sources, are commonly believed to satisfy the following: 1. There is no classical de Sitter solution with parallel sources. 2. Classical de Sitter solutions with intersecting sources are unstable. 3. Classical de Sitter solutions c…
Proves wave equation solutions in Kerr-de Sitter spacetime have specific asymptotic expansions.
problem Analyzing solutions to wave equations in Kerr-de Sitter spacetime.
method Developed a Fredholm setup for quasinormal modes and analyzed trapping of lightlike geodesics.
result Proves asymptotic expansions of wave equation solutions up to a decay order.
Study finds necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.
problem Understanding the asymptotic behavior of black hole geometries.
method Used hidden symmetry and conformal geometry technology to find necessary conditions.
result Necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.
Integrable flows on null curves in anti-de Sitter 3-space studied.
problem Analyzing integrable flows on null curves in anti-de Sitter 3-space.
method Formulated integrable flows related to the KdV hierarchy on null curves exploiting the geometry of anti-de Sitter 3-space.
result Explicitly found closed stationary solutions in terms of periodic solutions of a Lamé equation.
Proves uniqueness of certain spacetime solutions with extremal horizons.
problem Proving uniqueness of extremal Schwarzschild de Sitter spacetime solutions.
method Analytic proof in four and higher dimensions, spectral problem for hyperbolic surfaces.
result Proves extremal Schwarzschild de Sitter solutions are unique up to identifications.
Characterizes curves for minimal surfaces in de Sitter space.
problem Minimal surfaces in de Sitter space.
method Variational problem to find critical points of center of mass.
result Curves are critical points of center of mass.
Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately compactified space.
Adds charged black holes to de Sitter space.
problem Gluing charged black holes into de Sitter space.
method Extends Hintz's result to Einstein-Maxwell system with positive cosmological constant, using Reissner-Nordström or Kerr--Newman--de Sitter black holes.
result Determines conditions for gluing black holes into de Sitter space.
We construct dynamical many-black-hole spacetimes with well-controlled asymptotic behavior as solutions of the Einstein vacuum equation with positive cosmological constant. We accomplish this by gluing Schwarzschild-de Sitter or Kerr-de Sitter black hole metrics into neighborhoods of points on the future conformal boun…
Study of null mean curvature flow on de Sitter lightcone, related to 2d-Ricci flow.
problem Analyzing singularity formation and asymptotic behavior of null mean curvature flow.
method Rescaling procedure to relate to 2d-Ricci flow, singularity analysis, asymptotic behavior study.
result Ancient solutions to the flow can be understood in terms of 2d-Ricci flow.
In this paper we construct a parametrix for the forward fundamental solution of the wave and Klein-Gordon equations on asymptotically de Sitter spaces without caustics. We use this parametrix to obtain asymptotic expansions for solutions of the inhomogeneous equation and to obtain a uniform L^p estimate for a family of…
Geometric transformations on null curves in AdS induce KdV solutions.
problem Transforming null curves in AdS to solve KdV equations.
method Geometric transformations that induce Bäcklund transformations for KdV.
result Satisfies permutability theorem for null curves with constant bending.
In this paper, we consider the inverse hessian quotient curvature flow with star-shaped initial hypersurface in anti-de Sitter-Schwarzschild manifold. We prove that the solution exists for all time, and the second fundamental form converges to identity exponentially fast.
Establishes scattering theory for de Sitter vacuum solutions in even dimensions.
problem Quantitative nonlinear scattering theory for asymptotically de Sitter vacuum solutions in even spatial dimensions.
method Geometric Littlewood-Paley decomposition of the solution, constructing the scattering map.
result Existence and uniqueness of scattering states, asymptotic completeness, and invertible scattering map with quantitative control.
Uniqueness theorem for extremal charged black holes in de Sitter space.
problem Proving uniqueness of extremal charged black holes in de Sitter space.
method Analyzing Einstein-Maxwell theory with a positive cosmological constant.
result Local isometry to extremal Reissner-Nordström-de Sitter black hole or its near-horizon geometry.
Building upon the work of Brendle, Marques and Neves on the construction of counterexamples to Min-Oo's conjecture, we exhibit deformations of the de Sitter-Schwarzschild space of dimension n≥3 satisfying the dominant energy condition and agreeing with the standard metric along the event and cosmological horizons…
In this paper we study non-singular vacuum static space-times with non-zero cosmological constant. We introduce new integral quantities, and under suitable assumptions we prove their monotonicity along the level set flow of the static potential. We then show how to use these properties to derive a number of sharp geome…
In this global study of solutions to the linear wave equation on Schwarzschild de Sitter spacetimes we attend to the cosmological region of spacetime which is bounded in the past by cosmological horizons and to the future by a spacelike hypersurface at infinity. We prove an energy estimate capturing the expansion of th…
Classification of specific pseudo-Riemannian manifolds.
problem Classifying conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds.
method Complete classification through mathematical analysis.
result Conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds are either de Sitter or anti-de Sitter spacetimes.
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.
problem Optimal isoperimetric inequality for specific hypersurfaces in de Sitter space.
method Analyzes spacelike, compact, star-shaped, and 2-convex hypersurfaces in de Sitter space.
result Proves an optimal isoperimetric inequality for the specified hypersurfaces.
Study Lorentz harmonic maps and spacelike surfaces in anti-de Sitter space.
problem Analyzing the relationship between Lorentz harmonic maps and spacelike surfaces.
method Using loop group techniques, develop DPW-type representations and solve Cauchy problems.
result Establish a correspondence between Lorentz harmonic maps and spacelike immersions, leading to families of surfaces of constant Gauss curvature.
Proof of Tholozan's volume formula for anti-de-Sitter 3-manifolds.
problem Volume calculation for closed anti-de-Sitter 3-manifolds.
method Chern-Simons theory approach.
result Proof of Tholozan's volume formula.
Estimates for spacelike hypersurfaces in de Sitter space.
problem Isometric embedding problem in de Sitter space.
method Obtained Weyl-type estimates and closedness in the space of embeddings.
result Weyl-type estimates and closedness in the space of embeddings.
This paper addresses pure gauge questions in the study of (asymptotically) de Sitter spacetimes. We construct global solutions to the eikonal equation on de Sitter, whose level sets give rise to double null foliations, and give detailed estimates for the structure coefficients in this gauge. We show two results which a…
Link between Teichmüller and anti de Sitter geometry via length functions.
problem Understanding the geometry of Teichmüller space and anti de Sitter manifolds.
method Establishing a connection between Teichmüller space and anti de Sitter geometry through length functions.
result New purely anti de Sitter proofs of Teichmüller theory results.
Combines non-Euclidean and de Sitter geometries on the plane.
problem Exploring Penrose's Conformal Cyclic Cosmology.
method Geometric model combining Beltrami-Klein and de Sitter spaces.
result Discovery of hidden ${f G}_2$ symmetry in de Sitter spaces.
The paper classifies surfaces with constant curvature in 3D De Sitter and anti De Sitter spaces.
problem Classifying surfaces with constant curvature in 3D De Sitter and anti De Sitter spaces.
method Analyzing conditions equivalent to constant principal curvature, mean curvature, and second mean curvature.
result Surfaces of L1-2-type in De Sitter and anti De Sitter spaces are either standard products, scrolls, or have non-constant curvature properties. Formulas derived for operators on forms in anti-de Sitter spaces.
problem Operators on forms in anti-de Sitter spaces.
method Explicit formulas for codifferential and Laplace-de Rham operators.
result Formulas for restriction and continuation between spaces.
Study subelliptic heat kernel on octonionic anti-de Sitter space.
problem Heat kernel of octonionic anti-de Sitter space.
method Lift Laplacian of octonionic hyperbolic space and use sub-Laplacian.
result Two integral representations for subelliptic heat kernel.
New proof of stability for expanding Kerr-de Sitter spacetimes with smoothness at the boundary.
problem Stability of expanding region of Kerr-de Sitter spacetimes.
method Modified generalized harmonic gauge, local stability near conformal boundary, smoothness down to future conformal boundary.
result Smoothness of conformally rescaled metric down to future conformal boundary with mild singularity.
In this paper we propose and discuss a notion of mass for compact static metrics with positive cosmological constant. As a consequence, we characterise the de Sitter solution as the only static vacuum metric with zero mass. Finally, we show how to adapt our analysis to the case of negative cosmological constant, leadin…
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extendin…
Study flow on de Sitter space for convex hypersurfaces.
problem Behavior of locally constrained inverse curvature flow in de Sitter space.
method Analyze flow on de Sitter space with specific initial conditions and inequalities.
result Derive Alexandrov-Fenchel type inequalities.
Stability of black holes proven in full subextremal range with positive cosmological constant.
problem Stability of Kerr-de Sitter black holes in the full subextremal range.
method Similar to previous proof in slowly rotating case, with implementation of constraint damping and verification of subprincipal symbol condition.
result Stability of Kerr-de Sitter black holes proven in the full subextremal range.
Study domination between non-Fuchsian surface group representations and anti-de Sitter geometry.
problem Domination problem between non-Fuchsian representations of closed surface groups.
method Analysis of branched harmonic immersions and construction of anti-de Sitter 3-manifolds.
result Found that representations admitting branched harmonic immersions dominate other representations, and constructed large families of branched anti-de Sitter 3-manifolds.
Paper extends positive energy theorem to anti-de Sitter spacetimes.
problem Proving positive energy theorem for weighted anti-de Sitter spacetimes.
method Generalized positive energy theorem for 3D anti-de Sitter initial data sets.
result Positive energy theorem proved for weighted anti-de Sitter spacetimes.
Extends Hopf's theorem to de Sitter-Schwarzschild and Reissner-Nordstrom manifolds.
problem Finding constant mean curvature surfaces in specific spacetimes.
method Partial differential equations in the complex plane, generalizing holomorphy.
result Extends Hopf's theorem to new spacetime geometries.
Paper proves rigidity for certain spacelike hypersurfaces in de Sitter space.
problem Proving rigidity for hypersurfaces with curvature restrictions.
method Analogue to Guan and Shen's theorem for Riemannian space forms.
result Rigidity theorem for locally isometric hypersurfaces in de Sitter space.
We consider IIA compactifications on solvmanifolds with O6/D6 branes and study the conditions for obtaining de Sitter vacua in ten dimensions. While this is a popular set-up for searching de Sitter vacua, we propose a new method to include supersymmetry breaking sources. For space-time filling branes preserving bulk su…
Study on compact biconservative hypersurfaces in de Sitter space.
problem Understanding compact biconservative hypersurfaces in de Sitter space.
method Investigation of hypersurfaces with constant scalar curvature under geometric constraints.
result Extension of rigidity properties of biconservative hypersurfaces.
We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the initial data of a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole, then in a …
We prove Birkhoff-type results showing that L2 solutions of the linearized Einstein equations around Riemannian Kottler ("Schwarzschild-anti de Sitter") metrics in arbitrary dimension and horizon topology, which are not controlled by "master functions" are pure gauge. Together with earlier results this implies that …
Paper finds minimum volume for specific anti-de Sitter 3-manifolds.
problem Finding the minimum volume of globally hyperbolic anti-de Sitter 3-manifolds.
method Analyzes maximal globally hyperbolic Cauchy-compact anti-de Sitter 3-manifolds.
result Minimum volume is π²|χ(M)|, attained for Fuchsian manifolds.
Study classifies metrics on anti-de Sitter spacetime with specific symmetries.
problem Classifying metrics with specific symmetries on anti-de Sitter spacetime.
method Used classification techniques for pseudo-Riemannian and almost contact metric structures.
result Obtained classifications of homogeneous structures on anti-de Sitter spacetime.
Anti-de Sitter spacetimes with convex boundaries are uniquely determined by their boundary metrics.
problem Identifying anti-de Sitter spacetimes based on boundary properties.
method Proving rigidity for spacetimes with holonomy close to Fuchsian and convex boundaries.
result Globally hyperbolic compact anti-de Sitter spacetimes are determined by their boundary metrics.