In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity in terms of the isoperimetric function. We prove similar results for the linear filling radius inequality. Our theorems strengthen and gene...

We extend a theorem of Masur and Wolf which says that given a hyperbolic surface S, every isometry of the Teichmüller space for S with the Weil–Petersson metric is induced by an element of the mapping class group for S. Our argument handles the previously untreated cases of the four-holed sphere and the torus with one or two holes.

We discuss the dynamics of the correspondences associated to those plane curves whose local sections contract the Poincaré metric in a hyperbolic planar domain. 1. Introduction. We consider certain 1-dimensional, holomorphic correspondences of hyperbolic type, which we call " contractive curves. " These are curves whose local sections contract the Poincaré metric of a hyperbolic planar domain. ...

Let R be an n-dimensional Euclidean space and D be an n-dimensional hyperbolic space with the Poincaré metric for n > 1. In this paper, we shall prove the following results. (i) A bijection f : D → D n is an isometry (Möbius transformation) if and only if f is triangle preserving. (ii) A bijection f : R → R is an affine transformation if and only if f is triangle preserving.

We show that if a complete, doubling metric space is annularly linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a one-ended hyperbolic group has no local cut points, then its conformal dimension is greater than one.

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 Poincaré metric on hyperbolic space. As a result, we obtain non-trapping high energy estimates for this analytic continuation.

Keywords: Implicit iterative algorithm Asymptotically quasi-nonexpansive mappings Common fixed point Convex metric space a b s t r a c t In this paper, we consider an implicit iteration process to approximate the common fixed points of two finite families of asymptotically quasi-nonexpansive mappings in convex metric spaces. As a consequence of our result, we obtain some related convergence the...

in the present paper, we introduces the notion of integral type contractive mapping with respect to ordered s-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered s-metric space. moreover, we give an example to support our main result.

in this paper, we introduce the (g-$psi$) contraction in a metric space by using a graph.let $f,t$ be two multivalued mappings on $x.$ among other things, we obtain a common fixedpoint of the mappings $f,t$ in the metric space $x$ endowed with a graph $g.$

In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space (R with a metric of indefinite signature). We show that a graph is generically globally rigid in Euclidean space iff it is generically globally rigid in a complex or pseudo-Euclidean space. We also establish that global rig...