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Title: An enhanced uncertainty principle for the Vaserstein distance
Author: Carroll, Tom
Massaneda Clares, Francesc Xavier
Ortega Cerdà, Joaquim
Keywords: Teoria de la mesura geomètrica
Equacions en derivades parcials
Càlcul de variacions
Optimització matemàtica
Anàlisi global (Matemàtica)
Geometric measure theory
Partial differential equations
Calculus of variations
Mathematical optimization
Global analysis (Mathematics)
Issue Date: 13-Mar-2020
Publisher: London Mathematical Society
Abstract: Abstract. 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.
Note: Versió postprint del document publicat a:
It is part of: Bulletin of the London Mathematical Society, 2020, vol. 52, num. 6, p. 1158-1173
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ISSN: 0024-6093
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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