An enhanced uncertainty principle for the Vaserstein distance. Issue 6 (27th July 2020) - Carroll, Tom; Massaneda, Xavier; Ortega‐Cerdà, Joaquim
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.