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Lipschitz characterisation of polytopal Hilbert geometries. (English) Zbl 1331.52019

In this paper the author studies the Hilbert geometry of finite-dimensional convex polytopes. In particular he proves that an open convex domain \(C\subseteq\mathbb{R}^d\) not containing straight lines is a polytope if and only if, when endowed with its Hilbert distance, it is bi-Lipschitz equivalent to \(\mathbb{R}^d\) endowed with the Euclidean distance.
Reviewer: Marco Abate (Pisa)

MSC:

52B11 \(n\)-dimensional polytopes
51F99 Metric geometry
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References:

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