arXiv 2104.120972021-04math.DGmath.FAmath.MG

Wasserstein距离的不确定性估计、特征函数和下界

Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances

Nicolò De Ponti, Sara Farinelli

备注：: Major update. Structure of the proof simplified. Added new results on indeterminacy estimates for transport distances. The inequality between $p$-Wasserstein and $p$-Hellinger distances for $p>2$ is now not needed: it has been removed and will be part of a future project

摘要：

本文利用类似的技巧证明了${\sf RCD}(K,\infty)$空间中的两个不等式。第一个是不确定性估计，涉及$L^{\infty}$函数的正部分和负部分之间的$p$ -Wasserstein距离以及正部分和负部分之间的界面的度量。第二个是Laplace本征函数正负部分之间的$p$ -Wasserstein距离的一个严格下界。

英文摘要：

In the paper we prove two inequalities in the setting of ${\sf RCD}(K,\infty)$ spaces using similar techniques. The first one is an indeterminacy estimate involving the $p$-Wasserstein distance between the positive part and the negative part of an $L^{\infty}$ function and the measure of the interface between the positive part and the negative part. The second one is a conjectured lower bound on the $p$-Wasserstein distance between the positive and negative parts of a Laplace eigenfunction.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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