Carroll, TomMassaneda Clares, Francesc XavierOrtega Cerdà, Joaquim2020-12-072020-12-072020-03-130024-6093https://hdl.handle.net/2445/172580Abstract. We improve some recent results of Sagiv and Steinerberger that quantify the following uncertainty principle: for a function $f$ with mean zero, 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 the nodal set of the eigenfunction.16 p.application/pdfeng(c) London Mathematical Society, 2020Teoria de la mesura geomètricaEquacions en derivades parcialsCàlcul de variacionsOptimització matemàticaAnàlisi global (Matemàtica)Geometric measure theoryPartial differential equationsCalculus of variationsMathematical optimizationGlobal analysis (Mathematics)info:eu-repo/semantics/article7028462020-12-07info:eu-repo/semantics/openAccess