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arXiv · 1207.1342

Approximability of convex bodies and volume entropy in Hilbert geometry

Constantin Vernicos
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Abstract

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).

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Constantin Vernicos. 2012-07-05. Approximability of convex bodies and volume entropy in Hilbert geometry. https://doi.org/10.2140/pjm.2017.287.223

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