Brunn-Minkowski type inequalities for the lattice point enumerator

Iglesias, David; Zvavitch, Artem; Yepes Nicolás, Jesús

Publication:
Brunn-Minkowski type inequalities for the lattice point enumerator

dc.contributor.author	Iglesias, David
dc.contributor.author	Zvavitch, Artem
dc.contributor.author	Yepes Nicolás, Jesús
dc.contributor.department	Matemáticas
dc.contributor.other	Facultades de la UMU::Facultad de Matemáticas
dc.date.accessioned	2026-02-26T08:30:38Z
dc.date.available	2026-02-26T08:30:38Z
dc.date.copyright	© 2020 Elsevier Inc.
dc.date.created	2019
dc.date.issued	2020-08-26
dc.description.abstract	Geometric and functional Brunn-Minkowski type inequalities for the lattice point enumerator Gn(⋅) are provided. In particular, we show that Gn((1−λ)K+λL+(−1,1)^n)^{1/n}≥(1−λ)Gn(K)^{1/n}+λGn(L)^{1/n} for any non-empty bounded sets K,L⊂R^n and all λ∈(0,1). We also show that these new discrete versions imply the classical results, and discuss some links with other related inequalities.
dc.format	application/pdf
dc.identifier.citation	David Iglesias, Jesús Yepes Nicolás, Artem Zvavitch, Brunn-Minkowski type inequalities for the lattice point enumerator, Advances in Mathematics, Volume 370, 2020
dc.identifier.doi	https://doi.org/10.1016/j.aim.2020.107193.
dc.identifier.eissn	1090-2082
dc.identifier.issn	0001-8708
dc.identifier.uri	http://hdl.handle.net/10201/213981
dc.language	eng
dc.publisher	Elsevier
dc.relation	The first and second authors are partially supported by MICINN/FEDER project PGC2018-097046-B-I00 and “Programa de Ayudas a Grupos de Excelencia de la Región de Murcia”, Fundación Séneca, 19901/GERM/15. The third author is supported in part by the United States-Israel Binational Science Foundation(BSF) (number 2018115) and Simons Foundation (number 634219).
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/pii/S000187082030219X
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 International	*
dc.rights.accessRights	info:eu-repo/semantics/openAccess
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.subject	Brunn Minkowski inequality
dc.subject	Lattice point enumerator
dc.subject	Integer lattice
dc.subject	Borell Brascamp Lieb inequality
dc.subject.ods	No relacionado con ningún objetivo de desarrollo sostenible
dc.title	Brunn-Minkowski type inequalities for the lattice point enumerator
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/acceptedVersion
dspace.entity.type	Publication	es
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