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

被引：0

作者：

Kitagawa, Jun ^{[1
]}

Takatsu, Asuka ^{[2
,3
]}

机构：

[1] Michigan State Univ, Dept Math, E Lansing, MI USA

[2] Tokyo Metropolitan Univ, Dept Math Sci, Tokyo 1920397, Japan

[3] RIKEN Ctr Adv Intelligence Project AIP, Tokyo, Japan

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2025年

基金：

美国国家科学基金会;

关键词：

WASSERSTEIN DISTANCE; CONVERGENCE; POINTS; MAPS;

D O I：

10.1112/blms.70045

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：15

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