Polyhedral horofunction compactification as polyhedral ball
In this paper we answer positively a question raised by Kapovich and Leeb in a recent paper titled "Finsler bordifications of symmetric and certain locally symmetric spaces". Specifically, we show that for a finite-dimensional vector space with polyhedral norm, its horofunction compactific...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
2 Jul 2016
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| In: |
Arxiv
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| Online-Zugang: | Verlag, Volltext: http://arxiv.org/abs/1607.00564
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| Verfasserangaben: | Lizhen Ji and Anna-Sofie Schilling |
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| 520 | |a In this paper we answer positively a question raised by Kapovich and Leeb in a recent paper titled "Finsler bordifications of symmetric and certain locally symmetric spaces". Specifically, we show that for a finite-dimensional vector space with polyhedral norm, its horofunction compactification is homeomorphic to the dual unit ball of the norm by an explicit map. To prove this we establish a criterion for converging sequences in the horofunction compactification, and generalize the basic notion of the moment map in the theory of toric varieties. | ||
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