On discrete Brunn-Minkowski and isoperimetric type inequalities

Iglesias López, David; Lucas Marín, Eduardo; Yepes Nicolás, Jesús

Publication:
On discrete Brunn-Minkowski and isoperimetric type inequalities

dc.contributor.author	Iglesias López, David
dc.contributor.author	Lucas Marín, Eduardo
dc.contributor.author	Yepes Nicolás, Jesús
dc.contributor.department	Matemáticas
dc.date.accessioned	2026-02-26T17:24:02Z
dc.date.available	2026-02-26T17:24:02Z
dc.date.copyright	© 2021 Elsevier B.V.
dc.date.issued	2022-01
dc.description.abstract	We show that the lattice point enumerator Gn(·) satisfies G tK + sL + (−1,[t + s])n 1/n ≥ tG (K)1/n + sG (L)1/n for any K, L ⊂ Rn bounded sets with integer points and all t, s ≥ 0. We also prove that a certain family of compact sets, extending that of cubes [−m, m]n, with m ∈ N, minimizes the functional Gn(K + t[−1, 1]n), for any t ≥ 0, among those bounded sets K ⊂ Rn with given positive lattice point enumerator. Finally, we show that these new discrete inequalities imply the cor- responding classical Brunn-Minkowski and isoperimetric inequalities for non-empty compact sets.
dc.format	application/pdf
dc.format.extent	18
dc.identifier.citation	Discrete Mathematics Volume 345, Issue 1, January 2022, 112640
dc.identifier.doi	https://doi.org/10.1016/j.disc.2021.112640
dc.identifier.eissn	2578-9252
dc.identifier.issn	0012-365X
dc.identifier.uri	http://hdl.handle.net/10201/215121
dc.language	eng
dc.publisher	Elsevier
dc.relation	The work is partially supported by MICINN/FEDER project PGC2018-097046-B-I00 and by \Programa de Ayudas a Grupos de Excelencia de la Región de Murcia", Fundación Séneca, 19901/GERM/15.
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/pii/S0012365X21003538?via%3Dihub
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 Internacional
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	Isoperimetric inequality
dc.subject	Lattice point enumerator
dc.subject	Integer lattice
dc.subject.ods	No relacionado con ningún objetivo de desarrollo sostenible
dc.title	On discrete Brunn-Minkowski and isoperimetric type inequalities
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/acceptedVersion
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