In the paper we prove two inequalities in the setting of RCD(K, ∞) 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∞ 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.
De Ponti, N., Farinelli, S. (2022). Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 61(4) [10.1007/S00526-022-02240-5].
Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances
De Ponti, N
;
2022
Abstract
In the paper we prove two inequalities in the setting of RCD(K, ∞) 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∞ 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.
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