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Flag-approximability of convex bodies and volume growth of Hilbert geometries

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arxiv 1809.09471 v1 pith:DPGXWEUM submitted 2018-09-25 math.MG math.CO

Constantin Vernicos , Cormac Walsh This is my paper · ORCID
classification math.MGmath.CO
keywords convexvolumebodyflag-approximabilityasymptotichilbertallowsapproximate
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We introduce the flag-approximability of a convex body to measure how easy it is to approximate by polytopes. We show that the flag-approximability is exactly half the volume entropy of the Hilbert geometry on the body, and that both quantities are maximized when the convex body is a Euclidean ball. We also compute explicitly the asymptotic volume of a convex polytope, which allows us to prove that simplices have the least asymptotic volume.

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  1. On The Heine-Borel Property and Minimum Enclosing Balls

    cs.CG 2024-12 conditional novelty 5.0 of 10

    Minimum radius balls in metric spaces with the Heine-Borel property, including Hilbert, Thompson, and Funk geometries, are LP-type problems.

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