An enhanced uncertainty principle for the Vaserstein distance. Issue 6 (27th July 2020)

• Record Type: Journal Article
• Authors: Carroll, Tom; Massaneda, Xavier; Ortega‐Cerdà, Joaquim
• Is Part Of: Bulletin of the London Mathematical Society. Volume 52:Issue 6(2020)
• Page Start: 1158
• Page End: 1173
• Publication Date: 2020-07-27
• Subjects: 28A75 -- 35B05 -- 35P20 (primary) -- 49Q20 -- 58C40 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12390
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: We improve some recent results of Sagiv and Steinerberger that quantify the following uncertainty principle: for a function f with mean zero, then either the size of the zero set of the function or the cost of transporting the mass of the positive part of f to its negative part must be big. We also provide a sharp upper estimate of the transport cost of the positive part of an eigenfunction of the Laplacian. This proves a conjecture of Steinerberger and provides a lower bound of the size of a nodal set of the eigenfunction.