On discrete Lp Brunn–Minkowski type inequalities

Hernández Cifre, María de los Ángeles; Lucas Marín, Eduardo; Yepes Nicolás, Jesús

Publication:
On discrete Lp Brunn–Minkowski type inequalities

dc.contributor.author	Hernández Cifre, María de los Ángeles
dc.contributor.author	Lucas Marín, Eduardo
dc.contributor.author	Yepes Nicolás, Jesús
dc.contributor.department	Matemáticas
dc.contributor.other	Facultades de la UMU::Facultad de Matemáticas
dc.date.accessioned	2026-02-26T07:59:23Z
dc.date.available	2026-02-26T07:59:23Z
dc.date.copyright	© 2022, The Author(s)
dc.date.created	2021
dc.date.issued	2022-08-11
dc.description.abstract	Lp Brunn–Minkowski type inequalities for the lattice point enumerator Gn(·) are shown, p ≥ 1, both in a geometrical and in a functional setting. In particular, we prove that Gn((1 − λ) · K +p λ · L + (−1, 1)^n)^{p/n} ≥ (1 −λ)Gn(K)^{p/n} + λGn(L)^{p/n} for any K, L ⊂ R^n bounded sets with integer points and all λ ∈ (0, 1). We also show that these new discrete analogues (for Gn(·)) imply the corresponding results concerning the Lebesgue measure.
dc.format	application/pdf
dc.identifier.citation	Hernández Cifre, María A.; Lucas, Eduardo; Yepes Nicolás, Jesús. On discrete Lp Brunn-Minkowski type inequalities. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 116 (2022), no. 4, Paper No. 164, 14 pp.
dc.identifier.doi	https://doi.org/10.1007/s13398-022-01309-2
dc.identifier.issn	1578-7303
dc.identifier.uri	http://hdl.handle.net/10201/213841
dc.language	eng
dc.publisher	Springer
dc.relation	This research is part of the project PGC2018-097046-B-I00, supported by MCIN/AEI/10.13039/501100011033/FEDER “Una manera de hacer Europa”, and by “Programa de ayudas a grupos de excelencia de la Región de Murcia”, Fund. Séneca, 19901/GERM/15.
dc.relation.publisherversion	https://link.springer.com/article/10.1007/s13398-022-01309-2
dc.rights	Attribution 4.0 International	*
dc.rights.accessRights	info:eu-repo/semantics/openAccess
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	*
dc.subject	L p Brunn–Minkowski inequality, lattice point enumerator, p-sum, Borell–Brascamp–Lieb inequality
dc.subject	Brunn Minkowski inequality
dc.subject	Lattice point enumerator
dc.subject	P sum
dc.subject	Borell Brascamp Lieb inequality
dc.subject.ods	No relacionado con ningún objetivo de desarrollo sostenible
dc.title	On discrete Lp Brunn–Minkowski type inequalities
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/acceptedVersion
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