Further inequalities for the (generalized) Wills functional

Alonso Gutiérrez, David; Yepes Nicolás, Jesús; Hernández Cifre, María de los Ángeles

Publication:
Further inequalities for the (generalized) Wills functional

dc.contributor.author	Alonso Gutiérrez, David
dc.contributor.author	Yepes Nicolás, Jesús
dc.contributor.author	Hernández Cifre, María de los Ángeles
dc.contributor.department	Matemáticas
dc.contributor.other	Facultades de la UMU::Facultad de Matemáticas
dc.date.accessioned	2026-02-26T08:03:57Z
dc.date.available	2026-02-26T08:03:57Z
dc.date.created	2019
dc.date.issued	2020-03-05
dc.description.abstract	The Wills functional 𝒲(K) of a convex body K, defined as the sum of its intrinsic volumes Vi(K), turns out to have many interesting applications and properties. In this paper, we make profit of the fact that it can be represented as the integral of a log-concave function, which, furthermore, is the Asplund product of other two log-concave functions, and obtain new properties of the Wills functional (indeed, we will work in a more general setting). Among others, we get upper bounds for 𝒲(K) in terms of the volume of K, as well as Brunn–Minkowski and Rogers–Shephard-type inequalities for this functional. We also show that the cube of edge-length 2 maximizes 𝒲(K) among all 0-symmetric convex bodies in John position, and we reprove the well-known McMullen’s inequality 𝒲(K) ≤ e^{V1(K)} using a different approach.
dc.format	application/pdf
dc.identifier.citation	Alonso-Gutiérrez, David, Hernández Cifre, María A. and Yepes Nicolás, Jesús, Further inequalities for the (generalized) Wills functional, Communications in Contemporary Mathematics, Vol. 23, No. 03, 2050011 (2021)
dc.identifier.doi	https://doi.org/10.1142/S021919972050011X
dc.identifier.eissn	1793-6683
dc.identifier.uri	http://hdl.handle.net/10201/213861
dc.language	eng
dc.publisher	World Scientific Publishing
dc.relation	The work is partially supported by MICINN/FEDER projects MTM2016-77710-P and PGC2018-097046-B-I00, by DGA E26 17R and by “Programa de Ayudas a Grupos de Excelencia de la Región de Murcia”, Fundación Séneca, 19901/GERM/15.
dc.relation.publisherversion	https://www.worldscientific.com/doi/abs/10.1142/S021919972050011X
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	Wills functional
dc.subject	Intrinsic volumes
dc.subject	Log concave functions
dc.subject	Projection function
dc.subject	Asplund product
dc.subject	Brunn Minkowski type inequalities
dc.subject	Rogers Shephard type inequalities
dc.subject	John position McMullen’s inequality
dc.subject.ods	No relacionado con ningún objetivo de desarrollo sostenible
dc.title	Further inequalities for the (generalized) Wills functional
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/acceptedVersion
dspace.entity.type	Publication	es
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