论文标题
大小和霍尔姆斯 - 汤普森的内在体积
Magnitude and Holmes-Thompson intrinsic volumes of convex bodies
论文作者
论文摘要
幅度是紧凑型公制空间的数值不变，最初是受类别理论启发的，现在已知与其他无数几何量有关。概括早期的结果$ \ ell_1^n $和欧几里得空间，我们证明了在超赞式空间中的凸形体中的大小，就其Holmes-Thompson的固有体积而言。作为这种界限的应用，我们在Zonoid的情况下给出了Mahler猜想的简短证明，以及Sudakov的微型不平等。
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.
