Geodesic
Magnitude and Holmes–Thompson intrinsic volumes of convex bodies
Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 854-867

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DOI

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.
DOI : 10.4153/S0008439522000728
Mots-clés : magnitude, Holmes–Thompson intrinsic volumes, Mahler’s conjecture, Sudakov minoration 
Meckes, Mark W. Magnitude and Holmes–Thompson intrinsic volumes of convex bodies. Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 854-867. doi: 10.4153/S0008439522000728
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     title = {Magnitude and {Holmes{\textendash}Thompson} intrinsic volumes of convex bodies},
     journal = {Canadian mathematical bulletin},
     pages = {854--867},
     year = {2023},
     volume = {66},
     number = {3},
     doi = {10.4153/S0008439522000728},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000728/}
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