METRIC FOLIATIONS ON HYPERBOLIC SPACES

Constant curvature foliations in asymptotically hyperbolic spaces

Let (M, g) be an asymptotically hyperbolic manifold with a smooth conformal compactification. We establish a general correspondence between semilinear elliptic equations of scalar curvature type on ∂M and Weingarten foliations in some neighbourhood of infinity inM . We focus mostly on foliations where each leaf has constant mean curvature, though our results apply equally well to foliations whe...

Products of hyperbolic metric spaces

Products of hyperbolic metric spaces II

In [FS] we introduced a product construction for locally compact, complete , geodesic hyperbolic metric spaces. In the present paper we define the hyperbolic product for general Gromov-hyperbolic spaces. In the case of roughly geodesic spaces we also analyse the boundary at infinity.

A product construction for hyperbolic metric spaces

Given two pointed Gromov hyperbolic metric spaces (Xi, di, zi), i = 1, 2, and ∆ ∈ R+0 , we present a construction method, which yields another Gromov hyperbolic metric space Y∆ = Y∆((X1, d1, z1), (X2, d2, z2)). Moreover, it is shown that once (Xi, di) is roughly geodesic, i = 1, 2, then there exists a ∆′ ≥ 0 such that Y∆ also is roughly geodesic for all ∆ ≥ ∆ ′.

On metric spaces induced by fuzzy metric spaces

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...