Hilbert geometry of polytopes
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It is shown that the Hilbert metric on the interior of a convex polytope is bilipschitz to a normed vector space of the same dimension.
💡 Research Summary
The paper investigates the Hilbert metric defined on the interior of a convex polytope and establishes that this metric is bilipschitz equivalent to a normed vector space of the same dimension. The Hilbert distance d_H(x, y) between two interior points x and y of a convex set Ω ⊂ ℝⁿ is given by d_H(x, y) = ½ log(
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