A discrete approach to Zhang’s projection inequality

Alonso Gutiérrez, David; Lucas Marín, Eduardo; Martín Goñí, Javier

Publication:
A discrete approach to Zhang’s projection inequality

dc.contributor.author	Alonso Gutiérrez, David
dc.contributor.author	Lucas Marín, Eduardo
dc.contributor.author	Martín Goñí, Javier
dc.contributor.department	Matemáticas
dc.date.accessioned	2026-02-26T18:36:53Z
dc.date.available	2026-02-26T18:36:53Z
dc.date.copyright	© The Author(s), 2025
dc.date.issued	2025-09-24
dc.description.abstract	In this paper we will provide a new proof of the fact that for any convex body K ⊆ Rn 2n n n nn∞rn−1voln(K ∩ (ren + K))dr ≤0(voln(K))n+1,(voln−1(P ⊥ (K)))nn where (ei)n denotes the canonical orthonormal basis in Rn, P ⊥ (K) denotes n the orthogonal projection of K onto the linear hyperplane orthogonal to en, and volk denotes the k-dimensional Lebesgue measure. This inequality was proved by Gardner and Zhang and it implies Zhang’s inequality. We will use our new approach to this inequality in order to prove discrete analogues of this inequality and of an equivalent version of it, where we will consider the lattice point enumerator measure instead of the Lebesgue measure, and show that from such discrete analogues we can recover the aforementioned inequality and, therefore, Zhang’s inequality.
dc.format	application/pdf
dc.format.extent	45
dc.identifier.citation	Alonso-Gutiérrez D, Lucas Marín E, Martín Goñi J. A discrete approach to Zhang’s projection inequality. Canadian Journal of Mathematics. Published online 2025:1-47. doi:10.4153/S0008414X25101624
dc.identifier.doi	https://doi.org/10.4153/S0008414X25101624
dc.identifier.eissn	1496-4279
dc.identifier.issn	0008-414X
dc.identifier.uri	http://hdl.handle.net/10201/215201
dc.language	eng
dc.publisher	Cambridge University Press. Canadian Mathematical Society
dc.relation	The first author is supported by MICINN project PID2022-137294NB-I00 and DGA project E48 23R. The second author is funded by \Comunidad Autónoma de la Región de Murcia a través de la convocatoria de Ayudas a proyectos para el desarrollo de investigación científica y técnica por grupos competitivos, incluida en el Programa Regional de Fomento de la Investigación Científica y Técnica (Plan de Actuación 2022) de la Fundación Séneca-Agencia de Ciencia y Tecnologoía de la Región de Murcia, Ref.21899/PI/22". The third author is supported by the Austrian Science Fund (FWF) Project P32405 Asymptotic Geometric Analysis and Applications
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	Zhang's inequality
dc.subject	Berwald's inequality
dc.subject	Ball bodies
dc.subject	Covariogram function
dc.subject	Lattice point enumerator
dc.subject.ods	No relacionado con ningún objetivo de desarrollo sostenible
dc.title	A discrete approach to Zhang’s projection inequality
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/acceptedVersion
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