Intrinsic Quasi-Metrics

Warped product and quasi-Einstein metrics

Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...

Measurable metrics, intrinsic metrics and Lipschitz functions

In the paper [29], N. Weaver introduced the notion of measurable metric and that of Lipschitz function with respect to such a metric. The study of these notions was pursued by the same author in subsequent papers ([30, 32, · · ·]) and in the book [31]. In our paper [16], we treated various important examples and, in particular, we studied the intrinsic measurable metric associated with a local ...

Partial quasi-metrics

In this article we introduce and investigate the concept of a partial quasi-metric and some of its applications. We show that many important constructions studied in Matthews’s theory of partial metrics can still be used successfully in this more general setting. In particular we consider the bicompletion of the quasi-metric space that is associated with a partial quasi-metric space and study i...

Data mining for cones of metrics , quasi - metrics , m - hemi - metrics and ( m , s ) - super - metrics

INTRINSIC Lp METRICS FOR CONVEX BODIES

Intrinsic Lp metrics are defined and shown to satisfy a dimension–free bound with respect to the Hausdorff metric. MSC 2000: 52A20, 52A27, 52A40, 60G15.