Polyhedral Horofunction Compactification as a Polyhedral Ball

Lizhen Ji; Anna-Sofie Schilling

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arXiv · 1607.00564

Polyhedral Horofunction Compactification as a Polyhedral Ball

Lizhen Ji·Anna-Sofie Schilling

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Abstract

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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Lizhen Ji, Anna-Sofie Schilling. 2016-07-02. Polyhedral Horofunction Compactification as a Polyhedral Ball. https://arxiv.org/abs/1607.00564

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