The zoology of singularities for Lorentzian manifold is slightly more complicated than for Riemannian manifolds. Our present work study Cauchy-compact globally hyperbolic singular flat spacetimes with extreme BTZ-like singular lines. We use the notion of BTZ-extension of a singular spacetime introduced in a previous pa…
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10 results for “Cauchy-compact”
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.
Extending BTZ models to complete hyperbolic surfaces.
problem Extending BTZ models to complete hyperbolic surfaces.
method Proving a parametrization result for globally hyperbolic Cauchy-maximal and Cauchy-compact locally Minkowski manifolds with extreme BTZ.
result The tangent bundle of the Teichmüller space parametrizes globally hyperbolic Cauchy-maximal and Cauchy-compact locally Minkowski manifolds with extreme BTZ.
The study finds hypersurfaces with constant scalar curvature in Minkowski space.
problem Finding hypersurfaces with constant scalar curvature in Minkowski space.
method Analyzes regular domains in Minkowski space and constructs hypersurfaces with constant scalar curvature.
result Hypersurfaces with constant scalar curvature exist and provide foliations of domains.
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.
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…
Sur la géométrie de la singularité initiale des espaces-temps plats globalement hyperboliquesmath.DG
Let be a maximal globally hyperbolic Cauchy compact flat spacetime of dimension 2+1, admitting a Cauchy hypersurface diffeomorphic to a compact hyperbolic manifold. We study the asymptotic behaviour of level sets of quasi-concave time functions on . We give a positive answer to a conjecture of Benedetti and Guad…
Geometric approach to Dirac operator evolution on spacetimes.
problem Constructing the Cauchy evolution operator for Lorentzian Dirac operators.
method Realizing the operator as a sum of oscillatory integrals, relating to Feynman propagator.
result Relating Cauchy evolution operators to Feynman propagators and constructing Hadamard states.
Anti-de Sitter spacetimes embed cone-metrics as bent Cauchy surfaces.
problem Embedding cone-metrics in anti-de Sitter spacetimes.
method Proving embeddings using Fuchsian representations and GHMC spacetimes.
result Unique embeddings of cone-metrics in GHMC anti-de Sitter spacetimes.
Let be a compact, orientable surface of hyperbolic type. Let be a pair of negative numbers and let be a pair of marked metrics over of constant curvature equal to and respectively. Using a functional introduced by Bonsante, Mondello \& Schlenker, we show that there exists a …