凸体的大小和Holmes-Thompson内禀体积

IF 0.5 4区数学 Q3 MATHEMATICS

Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-06-06 DOI:10.4153/S0008439522000728

M. Meckes

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引用次数: 2

摘要

抽象量是紧致度量空间的一个数值不变量，最初受到范畴论的启发，现在已知与无数其他几何量有关。推广$\ell_1^n$和欧几里得空间中的早期结果，我们证明了超度量赋范空间中凸体的大小的上界，即其Holmes–Thompson本征体积。作为这个界的应用，我们给出了在zonoid和Sudakov的minorization不等式的情况下Mahler猜想的简短的新证明。

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Magnitude and Holmes–Thompson intrinsic volumes of convex bodies

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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来源期刊

Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The Canadian Mathematical Bulletin was established in 1958 to publish original, high-quality research papers in all branches of mathematics and to accommodate the growing demand for shorter research papers. The Bulletin is a companion publication to the Canadian Journal of Mathematics that publishes longer papers. New research papers are published continuously online and collated into print issues four times each year. To be submitted to the Bulletin, papers should be at most 18 pages long and may be written in English or in French. Longer papers should be submitted to the Canadian Journal of Mathematics. Fondé en 1958, le Bulletin canadien de mathématiques (BCM) publie des articles d’avant-garde et de grande qualité dans toutes les branches des mathématiques, de même que pour répondre à la demande croissante d’articles scientifiques plus brefs. Le BCM se veut une publication complémentaire au Journal canadien de mathématiques, qui publie de longs articles. En ligne, il propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés quatre fois par année. Les textes présentés au BCM doivent compter au plus 18 pages et être rédigés en anglais ou en français. C’est le Journal canadien de mathématiques qui reçoit les articles plus longs.