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Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances

TitleIndeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances
Publication TypeJournal Article
Year of Publication2022
AuthorsDe Ponti, N, Farinelli, S
Volume61
Issue4
Pagination131
Date Published2022/05/05
ISBN Number1432-0835
Abstract

In the paper we prove two inequalities in the setting of $$\mathsf {RCD}(K,\infty )$$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.

URLhttps://doi.org/10.1007/s00526-022-02240-5
Short TitleCalculus of Variations and Partial Differential Equations

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