Related papers: Staticity of Asymptotically Hyperbolic Minimal Mas…

This paper defines the pressure for asymptotically subadditive potentials under a mistake function, including the measuretheoretical and the topological versions. Using the advanced techniques of ergodic theory and topological dynamics, we…

Let $g$ be a smooth Riemannian metric on $\mathbb{S}^2$ and $H>0$ a constant. We establish an upper bound for the corresponding Bartnik mass $\mathfrak m_B(\mathbb{S}^2, g, H)$ assuming that the Gauss curvature $K_g$ is non-negative. Our…

We show that the asymptotic dimension of a hyperbolic relatively hyperbolic graph is finite provided that this holds true uniformly for the peripheral subgraphs and for the electrifiation. We use this to show that the asymptotic dimension…

We show that asymptotically hyperbolic initial data satisfying smallness conditions in dimensions $n\ge 3$, or fast decay conditions in $n\ge 5$, or a genericity condition in $n\ge 9$, can be deformed, by a deformation which is supported…

We show that a domain is an extension domain for a Haj\l asz-Besov or for a Haj\l asz-Triebel-Lizorkin space if and only if it satisfies a measure density condition. We use a modification of the Whitney extension where integral averages are…

We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all…

Gromov and Piatetski-Shapiro proved existence of finite volume non-arithmetic hyperbolic manifolds of any given dimension. In dimension four and higher, we show that there are about v^v such manifolds of volume at most v, considered up to…

In this paper we construct a parametrix for the high-energy asymptotics of the analytic continuation of the resolvent on a Riemannian manifold which is a small perturbation of the Poincar\'e metric on hyperbolic space. As a result, we…

We introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability. In particular, we prove that a non-improvable initial data set without local symmetries must sit inside a null…

We obtain explicit and simple conditions which in many cases allow one decide, whether or not a Denjoy domain endowed with the Poincare or quasihyperbolic metric is Gromov hyperbolic. The criteria are based on the Euclidean size of the…

We review notions of mass of asymptotically locally Anti-de Sitter three-dimensional spacetimes, and apply them to some known solutions. For two-dimensional general relativistic initial data sets the mass is not invariant under asymptotic…

We consider asymptotically hyperbolic manifolds whose metrics have Sobolev-class regularity, and introduce several technical tools for studying PDEs on such manifolds. Our results employ two novel families of function spaces suitable for…

We study relationships between asymptotic geometry of submanifolds in the hyperbolic space and their regularity properties near the ideal boundary, revisiting some of the related results in the literature. In particular, we discuss…

We solve the Jang equation with respect to asymptotically hyperbolic "hyperboloidal" initial data. The results are applied to give a non-spinor proof of the positive mass theorem in the asymptotically hyperbolic setting. This work focuses…

In this article, we extend Anderson's higher-dimensional Dehn filling construction to a large class of infinite-volume hyperbolic manifolds. This gives an infinite family of topologically distinct asymptotically hyperbolic Einstein…

Motivated by various applications and examples, the standard notion of potential for dynamical systems has been generalized to almost additive and asymptotically additive potential sequences, and the corresponding thermodynamic formalism,…

In this paper, we investigate some dynamical properties near a nonhyperbolic fixed point. Under some conditions on the higher nonlinear terms, we establish a stable manifold theorem and a degenerate Hartman theorem. Furthermore, the finite…

We study the existence and uniqueness of solutions to the static vacuum Einstein equations in bounded domains, satisfying the Bartnik boundary conditions of prescribed metric and mean curvature on the boundary.

V-static metrics generalise the notion of static metrics, and stem from the work of Miao and Tam [arXiv:0807.2693], and Corvino, Eichmair and Miao [arXiv:1211.6168] on critical points of the volume functional over the space of compact…

We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center…