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

Autor:	Vernicos, Constantin, Walsh, Cormac
Rok vydání:	2018
Předmět:	Mathematics - Metric Geometry Mathematics - Combinatorics 53C60 (primary) 52B05 53C24 58B20 53A20 (secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 15 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1809.09471 Zobrazit plný text záznamu View this record from Arxiv