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arXiv · 1705.01867

Fine approximation of convex bodies by polytopes

Márton Naszódi·Fedor Nazarov·Dmitry Ryabogin
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Abstract

We prove that for every convex body $K$ with the center of mass at the origin and every $\varepsilon\in \left(0,\frac{1}{2}\right)$, there exists a convex polytope $P$ with at most $e^{O(d)}\varepsilon^{-\frac{d-1}{2}}$ vertices such that $(1-\varepsilon)K\subset P\subset K$.

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Márton Naszódi, Fedor Nazarov, Dmitry Ryabogin. 2017-05-04. Fine approximation of convex bodies by polytopes. https://arxiv.org/abs/1705.01867

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