Fine approximation of convex bodies by polytopes
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 $(1-\varepsilon)K\subset P\subset K$.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2017
- DOI:
- 10.48550/arXiv.1705.01867
- arXiv:
- arXiv:1705.01867
- Bibcode:
- 2017arXiv170501867N
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 52B99
- E-Print:
- 12 pages, 5 figures