Related papers: Subdomain geometry of hyperbolic type metrics

We study the boundaries of relatively hyperbolic HHGs. Using the simplicial structure on the hierarchically hyperbolic boundary, we characterize both relative hyperbolicity and being thick of order 1 among HHGs. In the case of relatively…

An $n$-dimensional Hartogs domain $D_F$ with strongly pseudoconvex boundary can be equipped with a natural \K metric $g_F$. In this paper we prove that if $g_F$ is an extremal \K metric then $(D_F, g_F)$ is biholomorphically isometric to…

We study a class of two dimensional partially hyperbolic systems, not necessarily skew products, trying to establish the germ of a general theory. To illustrate the scope of the theory, we apply our results to the case of fast-slow…

We analyse the fine convergence properties of one parameter families of hyperbolic metrics, on a fixed underlying surface, that move always in a horizontal direction, i.e. orthogonal to the action of diffeomorphisms.

The point pair function $p_G$ defined in a domain $G\subsetneq\mathbb{R}^n$ is shown to be a quasi-metric and its other properties are studied. For a convex domain $G\subsetneq\mathbb{R}^n$, a new intrinsic quasi-metric called the function…

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…

We consider proper subdomains $G$ of $\mathbb{R}^n$ and their images $G'=f(G)$ under quasiconformal mappings $f$ of $\mathbb{R}^n$. We compare the distance ratio metrics of $G$ and $G'$; as an application we show that $\varphi$-uniform…

We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.

We study an intermittent quasistatic dynamical system composed of nonuniformly hyperbolic Pomeau--Manneville maps with time-dependent parameters. We prove an ergodic theorem which shows almost sure convergence of time averages in a certain…

We present a new criterion for the complex hyperbolicity of a non-compact quotient X of a bounded symmetric domain. For each p $\ge$ 1, this criterion gives a precise condition under which the subvarieties V $\subset$ X with dim V $\ge$ p…

We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.

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 propose a hyperbolic set-to-set distance measure for computing dissimilarity between sets in hyperbolic space. While point-to-point distances in hyperbolic space effectively capture hierarchical relationships between data points, many…

In the first part of this investigation, [Ha], we generalized a weighted distance function of [Li] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so-called M-relative metric are…

Motivated by spectral asymptotics for orbital integrals in a relative trace formula, we generalize a number of geometric properties of geodesics in the hyperbolic plane, to maximal flat submanifolds of symmetric spaces of non-compact type.

In this paper, we introduce the concept of quasihyperbolically visible spaces. As a tool, we study the connection between the Gromov boundary and the metric boundary.

In this paper, motivated by the work of Bonk, Heinonen, and Koskela (Asterisque, 2001), we consider the problem of the equivalence of the Gromov boundary and Euclidean boundary. Our strategy to study this problem comes from the recent work…

Object detection, for the most part, has been formulated in the euclidean space, where euclidean or spherical geodesic distances measure the similarity of an image region to an object class prototype. In this work, we study whether a…

A new similarity invariant metric $v_G$ is introduced. The visual angle metric $v_G$ is defined on a domain $G\subsetneq\Rn$ whose boundary is not a proper subset of a line. We find sharp bounds for $v_G$ in terms of the hyperbolic metric…

In this paper, we consider a scale invariant Cassinian metric and a Gromov hyperbolic metric. We discuss a distortion property of the scale invariant Cassinian metric under M\"obius maps of a punctured ball onto another punctured ball. We…