Accepted Paper

Inserted: 28 apr 2021
Last Updated: 28 apr 2022

Journal: Calculus of Variations and Partial Differential Equations
Year: 2021

Abstract:

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.

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