相关论文: Geometry of the quasi-hyperbolic Szekeres models
This paper is a revised version of arXiv:0805.0529 and Phys.Rev. D78, 064038 (2008), taking into account the erratum published in Phys.Rev. D85, 069903(E) (2012). Geometrical and topological properties of the quasi-plane Szekeres model and…
The quasispherical Szekeres metric is an exact solution to Einstein's equations describing an inhomogeneous and anisotropic cosmology. Though its governing equations are well-known, there are subtle, often-overlooked details in how the…
We study the properties and behaviour of the quasi-pseudospherical and quasi-planar Szekeres models, obtain the regularity conditions, and analyse their consequences. The quantities associated with "radius" and "mass" in the quasi-spherical…
In this paper, we continue our study of quasihyperbolic metric in Banach spaces. The main results of the paper present a criterion for smoothness of geodesics of quasihyperbolic type metrics in Banach spaces, under a Dini type condition on…
This is a tale describing the large scale geometry of Euclidean plane domains with their hyperbolic or quasihyperbolic distances. We prove that in any hyperbolic plane domain, hyperbolic and quasihyperbolic quasi-geodesics are the same…
This paper considers the volume averaging in the quasispherical Szekeres model. The volume averaging became of considerable interest after it was shown that the volume acceleration calculated within the averaging framework can be positive…
We characterize Gromov hyperbolicity of the quasihyperbolic metric space (\Omega,k) by geometric properties of the Ahlfors regular length metric measure space (\Omega,d,\mu). The characterizing properties are called the Gehring--Hayman…
We analyze the coarse geometry of the Weil-Petersson metric on Teichm\"uller space, focusing on applications to its synthetic geometry (in particular the behavior of geodesics). We settle the question of the strong relative hyperbolicity of…
We consider the quasihyperbolic metric, and its generalizations in both the $n$-dimensional Euclidean space $R^n$, and in Banach spaces. Historical background, applications, and our recent work on convexity properties of these metrics are…
Although the hyperbolic metric possesses many remarkable properties, it is not defined on arbitrary subdomains of $\mathbb{R}^n$ with $n \geq 2$. This article introduces a new hyperbolic-type metric that provides an alternative approach to…
In this paper, we introduce the concepts of short arc and length map in quasihyperbolic metric spaces, and obtain some geometric characterizations of Gromov hyperbolicity for quasihyperbolic metric spaces in terms of the properties of short…
Structure formation in the Szekeres model is investigated. Since the Szekeres model is an inhomogeneous model with no symmetries, it is possible to examine the interaction of neighboring structures and its impact on the growth of a density…
The quasi-spherical Szekeres dust solutions are a generalization of the spherically symmetric Lemaitre-Tolman-Bondi dust models where the spherical shells of constant mass are non-concentric. The quasi-spherical Szekeres dust solutions can…
We characterise hyperbolic groups in terms of quasigeodesics in the Cayley graph forming regular languages. We also obtain a quantitative characterisation of hyperbolicity of geodesic metric spaces by the non-existence of certain local…
We investigate properties of quasihyperbolic balls and geodesics in Euclidean and Banach spaces. Our main result is that in uniformly smooth Banach spaces a quasihyperbolic ball of a convex domain is $C^1$-smooth. The question about the…
During the past thirty years hyperbolic type metrics have become popular tools also in modern mapping theory, e.g., in the study of quasiconformal and quasiregular maps in the euclidean $n$-space. We study here several metrics that one way…
Cutting a hyperbolic surface X along a simple closed multi-geodesic results in a hyperbolic structure on the complementary subsurface. We study the distribution of the shapes of these subsurfaces in moduli space as boundary lengths go to…
Uniformly quasiconformally homogeneous domains in $\mathbb{R}^n$ carry a transitive collection of $K$-quasiconformal maps for a fixed $K\geq 1.$ In this paper, we study two questions in this setting. The first is to show that…
We solve for all Szekeres metrics that have a single Killing vector. For quasi hyperboloidal ($\epsilon = -1$) metrics, we find that translational symmetries are possible, but only in metrics that have shell crossings somewhere, while…
Hierarchically hyperbolic spaces (HHSs) are a large class of spaces that provide a unified framework for studying the mapping class group, right-angled Artin and Coxeter groups, and many 3--manifold groups. We investigate strongly…