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.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Anti-de Sitter manifolds”
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.
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.
Inverse curvature flow studied in anti-de Sitter-Schwarzschild manifold.
problem Analyzing curvature flow in a specific spacetime geometry.
method Inverse hessian quotient curvature flow with star-shaped initial hypersurface.
result The solution exists for all time and converges exponentially fast to the identity.
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.
The paper defines a new coordinate system for anti-de Sitter structures.
problem Understanding the geometry of anti-de Sitter spaces.
method Combining recent work on anti-de Sitter structures with classical theory.
result Introduced a coordinate system resembling Fenchel-Nielsen coordinates.
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.
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.
Study on eigenvalues of Laplacian on anti-de Sitter manifolds.
problem Distribution and stability of eigenvalues in pseudo-Riemannian geometry.
method Analysis of -eigenvalues on anti-de Sitter manifolds.
result Countably many -eigenvalues are stable under small deformations.
Study on linear independence of Poincaré series for anti-de Sitter 3-manifolds.
problem Linear independence of generalized Poincaré series for anti-de Sitter 3-manifolds.
method Analysis of eigenfunctions and Laplacian on anti-de Sitter 3-manifolds.
result Unbounded multiplicities of eigenvalues for -eigenfunctions and stable -eigenvalues.
Introduces Anti-de Sitter geometry and its connection to Teichmüller theory.
problem None explicitly stated, focuses on introducing concepts.
method Broad introduction to Anti-de Sitter geometry, focusing on dimension three and Teichmüller theory.
result Classification of maximal globally hyperbolic Cauchy compact manifolds and construction of the Gauss map.
Paper proves rigidity of certain manifold immersions into specific spacetimes.
problem Rigidity of isometric immersions into light cones.
method Analyzes Riemannian manifolds of dimension n-1 into light cones of n+1 spacetimes.
result Shows rigidity of isometric immersions for n ≥ 3.
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: …
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.
Study lightlike hypersurfaces in anti-de Sitter space.
problem Characterize singularities of lightlike hypersurfaces.
method Investigate lightlike hypersurfaces along spacelike submanifolds in anti-de Sitter space.
result Characterize singularities of lightlike hypersurfaces.
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.
Proves metrics of curvature ≤ -1 on surfaces are isometric to space-like convex surfaces in anti-de Sitter space.
problem Proving metrics of curvature ≤ -1 on closed surfaces.
method Approximation using isometric immersion of smooth metrics by Labourie--Schlenker.
result Any metric with curvature ≤ -1 on a closed surface is isometric to a space-like convex surface in anti-de Sitter space.
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 geodesics on Kerr-Newman instantons with de Sitter or anti-de Sitter asymptotics.
problem Characterize geodesics on Kerr-Newman instantons with specific asymptotic geometries.
method Use first integrals for the Hamilton-Jacobi equation to characterize trajectories.
result Characterized geodesics, including stable equilibrium orbits, in Kerr-Newman instantons with de Sitter or anti-de Sitter asymptotics.
The paper analyzes Gauss maps of Lorentzian surfaces in anti-de Sitter space.
problem Determining the type numbers of pseudo-hyperbolic Gauss maps of Lorentzian surfaces.
method Investigates the type numbers of pseudo-hyperbolic Gauss maps of oriented Lorentzian surfaces with constant curvatures in anti-de Sitter space.
result Investigates the behavior of type numbers of pseudo-hyperbolic Gauss maps along parallel families of surfaces.
Researchers classify differential operators for anti-de Sitter spaces.
problem Classifying differential operators intertwining representations of conformal vector fields.
method Constructing and classifying differential operators between spaces of differential forms.
result Classification of differential operators for anti-de Sitter spaces.
In this paper we provide a family of algebraic space-like surfaces in the three dimensional anti de Sitter space that shows that this Lorentzian manifold admits algebraic maximal examples of any order. Then, we classify all the space-like order two algebraic maximal hypersurfaces in the anti de Sitter -dimensional s…
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.
Degeneration of globally hyperbolic maximal anti-de Sitter structures along pinching sequencesmath.DG
Study pinching sequences to understand degeneration of anti-de Sitter structures.
problem Understanding the degeneration of anti-de Sitter structures along pinching sequences.
method Parameterization of deformation space and analysis of pinching sequences.
result Regular anti-de Sitter structures appear as limiting points.
Solves Dirichlet problem for prescribed scalar curvature in Anti-de Sitter space
problem Dirichlet problem for prescribed scalar curvature in Anti-de Sitter space
method Fully non-linear elliptic equation
result Solves if datas are strictly convex
Study of 2D Lorentzian anti-de Sitter plane using geometric control theory.
problem Understanding extremal trajectories and reachable set on anti-de Sitter plane.
method Geometric control theory and differential geometry.
result Construction of optimal synthesis and description of Lorentzian distance.
We establish the inequality for Henneaux-Teitelboim's total energy-momentum for asymptotically anti-de Sitter initial data sets which are asymptotic to arbitrary -slice in anti-de Sitter spacetime. In particular, when , it generalizes Chruściel-Maerten-Tod's inequality in the center of AdS mass coordinates. We …
Proves non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics.
problem Non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics.
method Analyzes linearised Einstein operator in -gauge for Kottler metrics.
result Non-degeneracy of -gauge-fixed linearised Einstein operator for most Riemannian Kottler metrics.
Study of longest arcs and cut loci in deformed anti de-Sitter spaces.
problem Existence and properties of time-like cycles in deformed Lorentzian manifolds.
method Analysis of universal covering, admissible curves, and Lorentzian geodesics.
result Identification of cut time and cut locus in deformed anti de-Sitter spaces.
Study null surfaces of pseudo-spherical curves in anti-de Sitter space.
problem Characterize null surfaces of pseudo-spherical spacelike framed curves in anti-de Sitter 3-space.
method Introduced nullcone fronts, classified singularities, defined Anti-de Sitter distance-squared functions.
result Relate singularities of nullcone fronts to those of framed curves.
Geometrically transitions hyperbolic to anti-de Sitter structures in 4D.
problem Creating geometric transitions between hyperbolic and anti-de Sitter structures in 4D.
method Deformation of hyperbolic 4-polytopes and joining with anti-de Sitter polytopes.
result Existence of geometric transition examples in 4D.
Study on constant mean curvature hypersurfaces in Anti-de Sitter space.
problem Characterizing and classifying hypersurfaces in Anti-de Sitter space.
method Analytic foliation and classification of hypersurfaces based on their asymptotic boundary.
result Every admissible sphere is the boundary of a unique hypersurface for any given mean curvature.
The paper defines almost strict domination for representations and connects it to anti-de Sitter 3-manifolds.
problem Defining and characterizing representations with specific properties.
method Using variational problems and harmonic maps to prove almost strict domination and construct representations.
result An almost strictly dominating pair of representations is equivalent to an anti-de Sitter 3-manifold with specific properties.
Study how geometric properties of anti-de Sitter structures degenerate along specific paths.
problem Degeneration of geometric properties in anti-de Sitter structures.
method Parameterization of deformation space by Teichmüller space, study of geometric quantities along quadratic differential rays.
result Geometric properties like Hausdorff dimension, core width, and Hölder exponent degenerate along specific paths.
The paper classifies actions on anti de Sitter spacetimes up to orbit equivalence.
problem Classifying cohomogeneity one actions on anti de Sitter spacetimes.
method Classification of actions by connected closed Lie subgroups of on .
result Classification up to orbit equivalence of actions by Lie subgroups of on .
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…
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…
Positive energy theorem for asymptotically anti-de Sitter spacetimes with distributional curvaturegr-qc
The positive energy theorem is proven for certain spacetimes with irregular curvature.
problem Proving the positive energy theorem for spacetimes with irregular curvature.
method Weak asymptotically anti-de Sitter initial data sets with distributional curvature under weak dominant energy condition.
result Positive energy theorem established for weakly irregular spacetimes.
Study - symbols linking anti-de Sitter tetrahedra to hyperbolic geometry.
problem Analyzing - symbols for quantum invariants.
method Examining asymptotics and analytic extensions of -symbols.
result Connection between anti-de Sitter tetrahedra and hyperbolic geometry.
New parameterizations for anti-de Sitter structures on surfaces.
problem Understanding deformation spaces of anti-de Sitter structures.
method Introducing regular globally hyperbolic structures and providing two parameterizations.
result Two parameterizations of deformation space of anti-de Sitter structures.
The horizontal heat kernel on the quaternionic anti de-Sitter spaces and related twistor spacesmath.DG
Study the heat kernel on quaternionic anti-de Sitter spaces and related spaces.
problem Understanding the heat kernel on quaternionic anti-de Sitter spaces and related spaces.
method Detailed study of the geometry, derivation of the horizontal Laplacian and subelliptic heat kernel formulas, derivation of small time asymptotics.
result Explicit formulas for the horizontal Laplacian and subelliptic heat kernel of the quaternionic anti-de Sitter fibration.
The paper studies the volume of Anti-de Sitter manifolds and their relation to Teichmüller space metrics.
problem Volume calculation of Anti-de Sitter maximal globally hyperbolic three-manifolds.
method Analyzes the volume in relation to Teichmüller space metrics and uses earthquake and measured geodesic lamination concepts.
result Volume coarsely behaves like the minima of the -energy of maps from to .
Study harmonic maps and anti-de Sitter 3-manifolds.
problem Existence and uniqueness of harmonic maps in infinite energy settings.
method Generalization of Corlette's result to infinite energy, analysis of asymptotic behavior, use of CAT(-1) Hadamard manifolds.
result Existence of new anti-de Sitter 3-manifolds.
Study on anti-de Sitter structures on surfaces with punctures.
problem Deformation of anti-de Sitter structures on surfaces with punctures.
method Parameterization of deformation space using Teichmüller spaces and quadratic differentials.
result Two parameterizations of the deformation space of wild globally hyperbolic anti-de Sitter structures.
The paper examines stability of Minkowski inequalities in warped product spaces.
problem Stability of Minkowski-type inequalities for hypersurfaces in warped product spaces.
method Established a stability estimate for the norm of the traceless second fundamental form.
result Proved stability of Minkowski inequalities in specific warped product examples.
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 -2-type in De Sitter and anti De Sitter spaces are either standard products, scrolls, or have non-constant curvature properties.
Study para-hyperKähler geometry of anti-de Sitter structures.
problem Understand the geometry of anti-de Sitter structures.
method Investigate para-hyperKähler structures and their relations.
result Found neutral pseudo-Riemannian metric and symplectic structures.