Title
Visible quasihyperbolic geodesics
Abstract
Given a metric space, there are several notions of it being negatively curved. In this talk, we single out a weak notion of negative curvature (which, in fact, is a consequence of strict negative sectional curvature in the Riemannian setting). This property is a form of visibility; the underlying metric spaces being bounded domains in R^n equipped with the quasihyperbolic distance. In this talk, we shall present a general criterion (a growth condition for the quasihyperbolic distance) ensuring visibility. We shall also present two applications of visibility property: (i) a natural identification between the Gromov boundary and Euclidean boundary and (ii) continuous boundary extension of quasiconformal maps. If time permits, we shall also discuss the comparison of visibility property of planar hyperbolic domains equipped with the hyperbolic and quasihyperbolic distances.
