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 sam...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
28.06.2023
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Subjects | |
Online Access | Get full text |
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Summary: | 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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DOI: | 10.48550/arxiv.2306.16239 |