Academic Journal
Magnitude and Holmes–Thompson intrinsic volumes of convex bodies: Magnitude and Holmes-Thompson intrinsic volumes of convex bodies
| Τίτλος: | Magnitude and Holmes–Thompson intrinsic volumes of convex bodies: Magnitude and Holmes-Thompson intrinsic volumes of convex bodies |
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| Συγγραφείς: | Meckes, Mark W. |
| Πηγή: | Canadian Mathematical Bulletin |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Canadian Mathematical Society, 2022. |
| Έτος έκδοσης: | 2022 |
| Θεματικοί όροι: | Random convex sets and integral geometry (aspects of convex geometry), Metric Geometry (math.MG), Mahler's conjecture, Convex sets in \(n\) dimensions (including convex hypersurfaces), Metric geometry, 01 natural sciences, Length, area, volume and convex sets (aspects of convex geometry), Functional Analysis (math.FA), Mathematics - Functional Analysis, Geometry and structure of normed linear spaces, Sudakov minoration, Mathematics - Metric Geometry, FOS: Mathematics, magnitude, 0101 mathematics, Holmes-Thompson intrinsic volumes |
| Περιγραφή: | 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. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml |
| Γλώσσα: | English |
| ISSN: | 1496-4287 0008-4395 |
| DOI: | 10.4153/s0008439522000728 |
| DOI: | 10.48550/arxiv.2206.02600 |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/abs/2206.02600 https://zbmath.org/7741836 https://doi.org/10.4153/s0008439522000728 |
| Rights: | CC BY arXiv Non-Exclusive Distribution |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....93cacf5b56d0e4ecd6e4b027fc48977e |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 14964287 00084395 |
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| DOI: | 10.4153/s0008439522000728 |