Products of hyperbolic metric spaces. (English) Zbl 1048.53027

Foertsch, Thomas; Schroeder, Viktor

Geom. Dedicata 102, 197-212 (2003).

The authors consider a pair of proper geodesic hyperbolic metric spaces, (which they define and motivate in the second section of their paper), and give a general procedure for the construction of a ‘hyperbolic product’ of these spaces which is itself a proper geodesic hyperbolic metric space. Contents include: an introduction; preliminaries (which include discussions of hyperbolicity, \(T\)-functions, the boundary at infinity and Busemann functions, and a Morse estimate); the hyperbolic product; and the boundary at infinity.

Reviewer: Joseph D. Zund (Las Cruces)

MSC:

53C21

Methods of global Riemannian geometry, including PDE methods; curvature restrictions

Keywords:

hyperbolic metric space; hyperbolic product