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2020-03-13

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/172580

An enhanced uncertainty principle for the Vaserstein distance

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https://doi.org/10.1112/blms.12390

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.

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Teoria de la mesura geomètrica, Equacions en derivades parcials, Càlcul de variacions, Optimització matemàtica, Anàlisi global (Matemàtica)

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Geometric measure theory, Partial differential equations, Calculus of variations, Mathematical optimization, Global analysis (Mathematics)

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CARROLL, Tom, MASSANEDA CLARES, Francesc Xavier and ORTEGA CERDÀ, Joaquim. An enhanced uncertainty principle for the Vaserstein distance. Bulletin of the London Mathematical Society. 2020. Vol. 52, num. 6, pags. 1158-1173. ISSN 0024-6093. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/172580

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