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arXiv · 2206.02600

Magnitude and Holmes-Thompson intrinsic volumes of convex bodies

Mark W. Meckes
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Abstract

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.

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Mark W. Meckes. 2022-06-06. Magnitude and Holmes-Thompson intrinsic volumes of convex bodies. https://doi.org/10.4153/s0008439522000728

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