Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances
Differential Geometry
2022-02-08 v2 Functional Analysis
Metric Geometry
Abstract
In the paper we prove two inequalities in the setting of spaces using similar techniques. The first one is an indeterminacy estimate involving the -Wasserstein distance between the positive part and the negative part of an 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 -Wasserstein distance between the positive and negative parts of a Laplace eigenfunction.
Cite
@article{arxiv.2104.12097,
title = {Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances},
author = {Nicolò De Ponti and Sara Farinelli},
journal= {arXiv preprint arXiv:2104.12097},
year = {2022}
}
Comments
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