000147754 001__ 147754 000147754 005__ 20250109150034.0 000147754 0247_ $$2doi$$a10.1142/S021919972050011X 000147754 0248_ $$2sideral$$a117491 000147754 037__ $$aART-2021-117491 000147754 041__ $$aeng 000147754 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso-Gutiérrez, David$$uUniversidad de Zaragoza 000147754 245__ $$aFurther inequalities for the (generalized) Wills functional 000147754 260__ $$c2021 000147754 5060_ $$aAccess copy available to the general public$$fUnrestricted 000147754 5203_ $$aThe Wills functional (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 (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 (K) among all 0-symmetric convex bodies in John position, and we reprove the well-known McMullen''s inequality (K) = eV1(K) using a different approach. 000147754 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E26-17R$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2016-77710-P$$9info:eu-repo/grantAgreement/ES/MICINN/PGC2018-097046-B-I00 000147754 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000147754 590__ $$a1.708$$b2021 000147754 591__ $$aMATHEMATICS$$b57 / 333 = 0.171$$c2021$$dQ1$$eT1 000147754 591__ $$aMATHEMATICS, APPLIED$$b101 / 267 = 0.378$$c2021$$dQ2$$eT2 000147754 592__ $$a1.36$$b2021 000147754 593__ $$aMathematics (miscellaneous)$$c2021$$dQ1 000147754 593__ $$aApplied Mathematics$$c2021$$dQ1 000147754 594__ $$a2.9$$b2021 000147754 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000147754 700__ $$aHernández Cifre, María A. 000147754 700__ $$aYepes Nicolás, Jesús 000147754 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000147754 773__ $$g23, 3 (2021), 2050011 [35 pp.]$$pCommun. Contemp. Math.$$tCommunications in Contemporary Mathematics$$x0219-1997 000147754 8564_ $$s419219$$uhttps://zaguan.unizar.es/record/147754/files/texto_completo.pdf$$yPostprint 000147754 8564_ $$s1539388$$uhttps://zaguan.unizar.es/record/147754/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000147754 909CO $$ooai:zaguan.unizar.es:147754$$particulos$$pdriver 000147754 951__ $$a2025-01-09-14:58:58 000147754 980__ $$aARTICLE