通过最优输运，以直径界划分球体的等面积分区

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-03-05 DOI:10.1112/blms.70045

Jun Kitagawa, Asuka Takatsu

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引用次数: 0

摘要

我们通过最优输运方法证明了单位球的等面积分区的存在性，并给出了用Monge-Kantorovich距离表示的直径界。当点从球体均匀采样时，这可以用来获得分区集最大直径的期望界。并给出了在计算切Monge-Kantorovich距离中的应用。

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Equal area partitions of the sphere with diameter bounds, via optimal transport

We prove existence of equal area partitions of the unit sphere via optimal transport methods, accompanied by diameter bounds written in terms of Monge–Kantorovich distances. This can be used to obtain bounds on the expectation of the maximum diameter of partition sets, when points are uniformly sampled from the sphere. An application to the computation of sliced Monge–Kantorovich distances is also presented.

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