A low-technology estimate in convex geometry
| dc.creator | Kuperberg, Greg | |
| dc.date | 1992-11-01 | |
| dc.date.accessioned | 2026-07-07T09:14:51Z | |
| dc.date.available | 2026-07-07T09:14:51Z | |
| dc.description | Let $K$ be an $n$-dimensional symmetric convex body with $n \ge 4$ and let $K\dual$ be its polar body. We present an elementary proof of the fact that $$(\Vol K)(\Vol K\dual)\ge \frac{b_n^2}{(\log_2 n)^n},$$ where $b_n$ is the volume of the Euclidean ball of radius 1. The inequality is asymptotically weaker than the estimate of Bourgain and Milman, which replaces the $\log_2 n$ by a constant. However, there is no known elementary proof of the Bourgain-Milman theorem. | |
| dc.description | The abstract is adapted from the Math Review by Keith Ball, MR 93h:52010 | |
| dc.identifier | https://arxiv.org/abs/math/9211216 | |
| dc.identifier | http://arxiv.org/abs/math/9211216 | |
| dc.identifier | Internat. Math. Res. Notices, 1992 (1992), no. 9, 181-183 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152823 | |
| dc.subject | Metric Geometry | |
| dc.subject | Functional Analysis | |
| dc.title | A low-technology estimate in convex geometry | |
| dc.type | text |