Related papers: Hyperbolic positive energy theorems

This is a survey on the analytic theory of linear wave equations on globally hyperbolic Lorentzian manifolds. There is no claim of originality.

A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…

We show that certain aspherical manifolds arising from hyperplane arrangements in negatively curved manifolds have relatively hyperbolic fundamental group.

We extend the validity of Brill's axisymmetric positive energy theorem to all asymptotically flat initial data sets with positive scalar curvature on simply connected manifolds.

This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints were never completed. This eprint is only an…

In this paper we study the asymptotic behavior of the analytic torsion for compact, oriented hyperbolic manifolds with respect to certain rays of representations obtained by restriction of irreducible representations of the group of…

The paper is concerned with positive solutions to problems of the type \begin{equation*} -\Delta_{\mathbb{B}^N} u - \lambda u = a(x) |u|^{p-1}\;u \, + \, f \, \;\;\text{in}\;\mathbb{B}^{N}, \quad u \in H^{1}{(\mathbb{B}^{N})},…

We prove the existence of infinitely many periodic orbits of symplectomorphisms isotopic to the identity if they admit at least one hyperbolic periodic orbit and satisfy some condition on the flux. Our result is proved for a certain class…

A generalized positive energy theorem for spaces with asymptotic SUSY compactification involving non-symmetric data is proved. This work is motivated by the work of Dai [D1][D2], Hertog-Horowitz-Maeda [HHM], and Zhang [Z].

By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their…

Consider the planar restricted $(N+1)$-body problem with trajectories of the $N(\ge 2)$ primaries forming a collision-free periodic solution of the $N$-body problem, for any positive energy $h$ and directions $\theta_{\pm} \in [0, 2\pi)$,…

We prove that the scattering matrix at all energies restricted to an open subset of the boundary determines an asymptotically hyperbolic manifold modulo isometries that are equal to the identity on the open subset where the scattering…

We generalize Bangert's non-hyperbolicity result for uniformly tamed almost complex structures on standard symplectic $R^{2n}$ to asymtotically standard symplectic manifolds.

In this paper, we discuss the birational invariance of the class of balanced hyperbolic manifolds.

Here we study the nonlinear hyperbolic equations of the type of equations from theory of flows on networks, for which we prove the solvability theorem under the appropriate conditions and also investigate the behaviour of the solution.

We prove positive mass theorem with angular momentum and charges for axially symmetric, simply connected, maximal, complete initial data sets with two ends, one designated asymptotically flat and the other either (Kaluza-Klein)…

We will provide bounds on both the Betti numbers and the torsion part of the homology of hyperbolic orbifolds. These bounds are linear in the volume and are a direct consequence of an efficient simplicial model of the thick part, which we…

In this paper we prove a characterization of $p$-hyperbolic ends on complete Riemannian manifolds which carries a Sobolev type inequality.

The purpose of the present paper is to prove existence of super-exponentially many compact orientable hyperbolic arithmetic $n$-manifolds that are geometric boundaries of compact orientable hyperbolic $(n+1)$-manifolds, for any $n \geq 2$,…

We consider a class of parabolic equations with critical electromagnetic potentials, for which we obtain a classification of local asymptotics, unique continuation results, and an integral representation formula for solutions.