Magnitude and Holmes-Thompson intrinsic volumes of convex bodies
| Autor: | Meckes, Mark W. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4153/S0008439522000728 |
| Popis: | Magnitude is a numerical invariant of compact metric spaces, originally inspired by category theory and now known to be related to myriad other geometric quantities. Generalizing earlier results in $\ell_1^n$ and Euclidean space, we prove an upper bound for the magnitude of a convex body in a hypermetric normed space in terms of its Holmes-Thompson intrinsic volumes. As applications of this bound, we give short new proofs of Mahler's conjecture in the case of a zonoid, and Sudakov's minoration inequality. Comment: v3: minor expositional clarifications. To appear in the Canadian Mathematical Bulletin |
| Databáze: | arXiv |
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