Abstract
AbstractIn the paper we prove two inequalities in the setting of $$\mathsf {RCD}(K,\infty )$$
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 $$L^{\infty }$$
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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
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