Polyhedral horofunction compactification as a polyhedral ball
In this paper we answer positively a question raised by Kapovich and Leeb in a paper titled “Finsler bordifications of symmetric and certain locally symmetric spaces”. Specifically, we show that for a finite-dimensional vector space with a polyhedral norm, its horofunction compactification is homeom...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
28 April 2025
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| In: |
The Asian journal of mathematics
Year: 2025, Jahrgang: 29, Heft: 1, Pages: 1-26 |
| ISSN: | 1945-0036 |
| DOI: | 10.4310/AJM.250429053604 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.4310/AJM.250429053604 Verlag, lizenzpflichtig, Volltext: https://intlpress.com/JDetail/1916970336413335554 
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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 paper titled “Finsler bordifications of symmetric and certain locally symmetric spaces”. Specifically, we show that for a finite-dimensional vector space with a 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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