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http://hdl.handle.net/2445/172580
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: https://doi.org/10.1112/blms.12390 |
It is part of: | Bulletin of the London Mathematical Society, 2020, vol. 52, num. 6, p. 1158-1173 |
URI: | http://hdl.handle.net/2445/172580 |
Related resource: | https://doi.org/10.1112/blms.12390 |
ISSN: | 0024-6093 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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702846.pdf | 224.78 kB | Adobe PDF | View/Open |
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