Heisenberg群上的多边际最优输运

IF 0.6 Q4 MATHEMATICS, APPLIED

Methods and applications of analysis Pub Date : 2020-03-24 DOI:10.4310/maa.2021.v28.n1.a5

Brendan Pass, A. Pinamonti, Mattia Vedovato

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引用次数: 2

摘要

我们考虑在Heisenberg群上对齐几个紧支撑的边缘以最小化总成本的多边缘最优传输，我们将总成本取为从边缘点到其质心的carnot - cartheodory距离的平方之和。在一定的技术假设下，证明了最优映射的存在唯一性。我们还指出了几个相关的悬而未决的问题。

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Multi-marginal optimal transport on the Heisenberg group

We consider the multi-marginal optimal transport of aligning several compactly supported marginals on the Heisenberg group to minimize the total cost, which we take to be the sum of the squared Carnot-Caratheodory distances from the marginal points to their barycenter. Under certain technical hypotheses, we prove existence and uniqueness of optimal maps. We also point out several related open questions.

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来源期刊

Methods and applications of analysis MATHEMATICS, APPLIED-

自引率

33.30%

发文量