论文标题

在海森堡集团上的多边界最佳运输

Multi-marginal optimal transport on the Heisenberg group

论文作者

Pass, Brendan, Pinamonti, Andrea, Vedovato, Mattia

论文摘要

我们考虑了在海森堡组上对齐几个紧凑​​型边际边缘的多边界最佳运输,以最大程度地降低总成本,我们认为这是从边际点到他们的男性中心的平方carnot-carthéodory距离的总和。在某些技术假设下,我们证明了最佳地图的存在和独特性。我们还指出了几个相关的开放问题。

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-Carathéodory 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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