UZH-Logo

Maintenance Infos

Minkowski versus Euclidean rank for products of metric spaces


Foertsch, T; Schroeder, V (2002). Minkowski versus Euclidean rank for products of metric spaces. Advances in Geometry, 2(2):123-131.

Abstract

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.

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.

Citations

3 citations in Web of Science®
4 citations in Scopus®
Google Scholar™

Altmetrics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Euclidean rank of metric spaces; Minkowski rank of metric spaces
Language:English
Date:2002
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:De Gruyter
ISSN:1615-715X
Free access at:Related URL. An embargo period may apply.
Publisher DOI:10.1515/advg.2002.002
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1895343
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0988.53033
http://front.math.ucdavis.edu/0102.5107 (Organisation)

Download

Full text not available from this repository.View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations