the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

The hyperbolic plane is an example of a geometry where the first four of Euclid’s Axioms hold but the fifth, the parallel postulate, fails and is replaced by a hyperbolic alternative. We discuss some basic properties of hyperbolic space, including how to coordinatize and measure lengths. We then consider the possibility of isometrically immersing the hyperbolic plane into 3 in such a way that l...

We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In an article by Grubǐsić and Moncrief, a formal expansion of solutions in the direction toward the singularity was proposed. Later, Kichenassamy and Rendall constructed a family of real analyti...

The Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-Hara/Monteiro and the Nesterov-Todd search directions have been used in many primal-dual interior-point methods for semide nite programs. This paper proposes an e cient method for computing the two directions when a semide nite program to be solved is large scale and sparse.

δ-Hyperbolic metric spaces have been defined by M. Gromov in 1987 via a simple 4-point condition: for any four points u, v, w, x, the two larger of the distance sums d(u, v)+ d(w, x), d(u, w) + d(v, x), d(u, x) + d(v, w) differ by at most 2δ. They play an important role in geometric group theory, geometry of negatively curved spaces, and have recently become of interest in several domains of co...

A plane domain Ω with more than one boundary point admits a hyperbolic metric and with respect to this metric, every holomorphic map of Ω into a subdomain X ⊆ Ω is a contraction. In this paper we define a new metric for the image domain X that is greater than or equal to the hyperbolic metric. Like the hyperbolic metric it has the property that any holomorphic map from Ω into X is a contraction...