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Horofunction compactifications and duality

Lemmens, Bas, Power, Kieran (2021) Horofunction compactifications and duality. arXiv.org, . (KAR id:90294)

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Abstract

We study the global topology of the horofunction compactification of smooth manifolds with a Finsler distance. The main goal is to show, for certain classes of these spaces, that the horofunction compactification is naturally homeomorphic to the closed unit ball of the dual norm of the norm in the tangent space (at the base point) that generates the Finsler distance. We construct explicit homeomorphisms for a variety of spaces in three settings: bounded convex domains in ℂ^n with the Kobayashi distance, Hilbert geometries, and finite dimensional normed spaces. For the spaces under consideration, the horofunction boundary has an intrinsic partition into so called parts. The natural connection with the dual norm arises through the fact that the homeomorphism maps each part in the horofunction boundary onto the relative interior of a boundary face of the dual unit ball. For normed spaces the connection between the global topology of the horofunction boundary and the dual norm was suggested by Kapovich and Leeb. We confirm this connection for Euclidean Jordan algebras equipped with the spectral norm.

Item Type: Article
Uncontrolled keywords: horofunction compactification; Finsler distance
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA440 Geometry
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Bas Lemmens
Date Deposited: 22 Sep 2021 13:42 UTC
Last Modified: 23 Sep 2021 08:38 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/90294 (The current URI for this page, for reference purposes)
Lemmens, Bas: https://orcid.org/0000-0001-6713-7683
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