Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances

In the paper we prove two inequalities in the setting of RCD(K, infinity) 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-infinity 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.

Automated summary

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