%0 Journal Article %D 2022 %T Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances %A Nicolò De Ponti %A Sara Farinelli %X

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.

%V 61 %P 131 %8 2022/05/05 %@ 1432-0835 %G eng %U https://doi.org/10.1007/s00526-022-02240-5 %N 4 %! Calculus of Variations and Partial Differential Equations