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arXiv · 1809.09471

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

Constantin Vernicos·Cormac Walsh
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Abstract

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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Constantin Vernicos, Cormac Walsh. 2018-09-25. Flag-approximability of convex bodies and volume growth of Hilbert geometries. https://arxiv.org/abs/1809.09471

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