Approximability of convex bodies and volume entropy in Hilbert geometry

Autor:	Vernicos, Constantin
Rok vydání:	2012
Předmět:	Mathematics - Metric Geometry Mathematics - Differential Geometry Mathematics - Symplectic Geometry 53C60 53C24 58B20 53A20
Zdroj:	Pacific J. Math. 287 (2017) 223-256
Druh dokumentu:	Working Paper
DOI:	10.2140/pjm.2017.287.223
Popis:	The approximability of a convex body is a number which measures the difficulty to approximate that body by polytopes. We prove that twice the approximability is equal to the volume entropy for a Hilbert geometry in dimension two end three and that in higher dimension it is a lower bound of the entropy. As a corollary we solve the entropy upper bound conjecture in dimension three and give a new proof in dimension two from the one found in Berck-Bernig-Vernicos (arXiv:0810.1123v2, published). Comment: 33 pages, 7 figures. Exposition improved, paper accepted for publication in pacific
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1207.1342 Zobrazit plný text záznamu View this record from Arxiv