Mass non-concentration at the nodal set and a sharp Wasserstein uncertainty principle

2021/03/22 by Mayukh Mukherjee, Mukherjee, Mayukh
Mathematics · Economics, Econometrics and Finance · #Numerical methods in inverse problems #Geometric Analysis and Curvature Flows #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2103.11633

Abstract

We prove L^p-mass concentration properties of Laplace eigenfunctions away from their nodal sets, extending a recent result in \citeGM3 to all dimensions, and giving a slight refinement of a result in \citeJN. As a consequence, we are able to derive a sharp Wasserstein uncertainty principle that holds uniformly in the high frequency regime, proving a conjecture in \citeSt1.

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