Related papers: A Toponogov globalisation result for Lorentzian le…

We introduce a canonical, compact topology, which we call weakly causal, naturally generated by the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by certain problems of quantum gravity. We show…

We introduce a hypertopology, induced by an inframetric up to full quantum isometry, on the class of pointed proper quantum metric spaces, which are separable, possibly non-unital, C*-algebras endowed with an analogue of the Lipschitz…

We prove sandwich theorems and a Tauberian theorem in the space of compact metric measure spaces, endowed with the Gromov-Hausdorff-Prokhorov (GHP) topology. These results hold with respect to a close relative of Gromov's Lipschitz order.…

The scheme of using the Chern-Simons action to regularize the gravitational Hamiltonian constraint is extended to including the Lorentzian term in the $k=0$ cosmological model. The Euclidean term and the Lorenzian term are thus regularized…

The constructive method of conformal blocks is developed for the construction of global solutions for two-dimensional metrics having one Killing vector. The method is proved to yeild a smooth universal covering space with a smooth…

The aim of the present paper is to establish a global theory of conformal changes in Finsler geometry. Under this change, we obtain the relationships between the most important geometric objects associated to $(M,L)$ and the corresponding…

How should one define metric space notions of convergence for sequences of spacetimes? Since a Lorentzian manifold does not define a metric space directly, the uniform convergence, Gromov-Hausdorff (GH) convergence, and Sormani-Wenger…

For a finitely generated group $G$, we introduce an asymmetric pseudometric on projectivized deformation spaces of $G$-trees, using stretching factors of $G$-equivariant Lipschitz maps, that generalizes the Lipschitz metric on Outer space…

In the first part of this work we show a uniqueness result for globally hyperbolic spacetimes with a spacelike conformal boundary satisfying the vacuum Einstein equations with positive cosmological constant. Then we present applications of…

Herein we present open problems and survey examples and theorems concerning sequences of Riemannian manifolds with uniform lower bounds on scalar curvature and their limit spaces. Examples of Gromov and of Ilmanen which naturally ought to…

We revisit certain path-lifting and path-continuation properties of abstract maps as described in the work of F. Browder and R. Rheindboldt in 1950-1960s, and apply their elegant theory to exponential maps. We obtain thereby a number of…

In [7] Klainerman introduced the hyperboloidal method to prove the global existence results for nonlinear Klein-Gordon equations by using commuting vector fields. In this paper, we extend the hyperboloidal method from Minkowski space to…

We characterize those spacetimes which admit a isometric (or conformal) embedding in some Lorentz-Minkowski space L^N. In particular, any globally hyperbolic spacetime can be isometrically embedded in L^N. This is proven by a result of its…

What is the analogous notion of Gromov-Hausdorff convergence for sequences of spacetimes? Since a Lorentzian manifold is not inherently a metric space, one cannot simply use the traditional definition. One approach offered by Sormani and…

The Lott-Sturm-Villani Curvature-Dimension condition provides a synthetic notion for a metric-measure space to have Ricci-curvature bounded from below and dimension bounded from above. We prove that it is enough to verify this condition…

We develop a suitable generalization of Almgren's theory of varifolds in a lorentzian setting, focusing on area, first variation, rectifiability, compactness and closure issues. Motivated by the asymptotic behaviour of the scaled hyperbolic…

I characterize the Lorentzian manifolds properly isometrically embeddable in Minkowski spacetime (i.e. the Lorentzian submanifolds of Minkowski spacetime that are also closed subsets). Moreover, I prove that the Lorentzian manifolds that…

We prove that for continuous Lorentz-Finsler spaces timelike completeness implies inextendibility. Furthermore, we prove that under suitable locally Lipschitz conditions on the Finsler fundamental function the continuous causal curves that…

We give a proof of an unpublished result of Thurston showing that given any hyperbolic metric on a surface of finite type with nonempty boundary, there exists another hyperbolic metric on the same surface for which the lengths of all simple…

We consider general relativity with cosmological constant minimally coupled to the electromagnetic field and assume that the four-dimensional space-time manifold is a warped product of two surfaces with Lorentzian and Euclidean signature…