Minkowski- versus Euclidean rank for products of metric spaces

Details Minkowski- versus Euclidean rank for products of metric spaces Minkowski- versus Euclidean rank for products of metric spaces

2001-02-14

arxiv.org/abs/math/0102107v1

Mathematics

Metric Geometry

20 pages, 1 figure

Scientific paper

We introduce a notion of the Euclidean- and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with respect to metric products, while additivity of the Euclidean rank only holds under additional assumptions, e.g. for Riemannian manifolds. We also study products with nonstandard product metrics.

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