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Hilbert metrics and Minkowski norms
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2005 (English)In: Journal of Geometry, ISSN 0047-2468, E-ISSN 1420-8997, Vol. 83, no 1-2, 22-31 p.Article in journal (Refereed) Published
Abstract [en]

It is shown that the Hilbert geometry (D,h D ) associated to a bounded convex domain D ⊂ double struck E signn is isometric to a normed vector space (V,∥ ̇ ∥) if and only if D is an open n-simplex. One further result on the asymptotic geometry of Hilbert's metric is obtained with corollaries for the behavior of geodesics. Finally we prove that every geodesic ray in a Hilbert geometry converges to a point of the boundary.

Place, publisher, year, edition, pages
2005. Vol. 83, no 1-2, 22-31 p.
Keyword [en]
Asymptotic geometry, Hilbert metric
National Category
Geometry
Identifiers
URN: urn:nbn:se:kth:diva-156520DOI: 10.1007/s00022-005-0005-1Scopus ID: 2-s2.0-29644433138OAI: oai:DiVA.org:kth-156520DiVA: diva2:767259
Note

QC 20141201

Available from: 2014-12-01 Created: 2014-11-28 Last updated: 2017-12-05Bibliographically approved

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