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.
Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances / De Ponti, N; Farinelli, S. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 1432-0835. - 61:4(2022), pp. 1-17. [10.1007/s00526-022-02240-5]
Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances
De Ponti, N
;Farinelli, S
2022-01-01
Abstract
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.| File | Dimensione | Formato | |
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