Related papers: On Asymptotically Locally Hyperbolic Metrics with …
We prove that all hierarchically hyperbolic spaces have finite asymptotic dimension and obtain strong bounds on these dimensions. One application of this result is to obtain the sharpest known bound on the asymptotic dimension of the…
This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…
Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…
We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal K\"{a}hler manifold with constant nonpositive holomorphic sectional curvature is…
Asymptotic symmetries of electric and magnetic Carrollian gravitational theories with a negative cosmological constant $\Lambda$ are analyzed in 3+1 space-time dimensions. In the magnetic theory, the asymptotic symmetry algebra is given by…
It is shown that within conformally flat stationary axisymmetric spacetimes, besides of the static family, there exists a new class of metrics, which is always stationary and axisymmetric. All these spacetimes, the static and the stationary…
We prove an asymptotic stability result for a linear coupled hyperbolic-elliptic system on a large class of singular background spacetimes in CMC gauge on the n-torus. At each spatial point these background spacetimes are perturbations of…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…
Static, spherically symmetric solutions with regular origin are investigated of the Einstein-Yang-Mills theory with a negative cosmological constant $\Lambda$. A combination of numerical and analytical methods leads to a clear picture of…
It is shown that various pathological properties of spacetimes can be explained by the presence of negative mass, including the cases when the total mass of the solution is a positive quantity. As an illustration, we consider several…
We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The spacetime is regular everywhere except on the symmetry axis where it possess a true curvature…
Substatic Riemannian manifolds with minimal boundary arise naturally in General Relativity as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, they constitute a vast generalization of nonnegative Ricci…
We demonstrate that the volume-renormalized mass for asymptotically hyperbolic manifolds recently introduced by the authors can be deduced from a reduced Hamiltonian perspective. In order to do this, we first use Michel's formalism of mass…
Hyperbolic monopole solutions can be obtained from circle-invariant ADHM data if the curvature of hyperbolic space is suitably tuned. Here we give explicit ADHM data corresponding to axial hyperbolic monopoles in a simple, tractable form,…
We investigate self-similar solutions which are asymptotic to the Friedmann universe at spatial infinity and contain a scalar field with potential. The potential is required to be exponential by self-similarity. It is found that there are…
For each degree p, we construct on any closed manifold a family of Riemannian metrics, with fixed volume such that any positive eigenvalues of the rough and Hodge Laplacians acting on differential p-forms converge to zero. In particular, on…
We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics,…
We establish the existence of infinitely many complete metrics with constant scalar curvature on prescribed conformal classes on certain noncompact product manifolds. These include products of closed manifolds with constant positive scalar…
In this paper, we study the regularity of asymptotically hyperbolic metrics with Einstein condition near boundary and Weyl curvature smooth enough in arbitrary dimension. Following Michael Anderson's method, we show that $C^{m,\alpha}$…