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Products of hyperbolic metric spaces. (English) Zbl 1048.53027

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.

MSC:

53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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