146910 20241129141114.0 doi 10.1016/j.jmaa.2024.129065 sideral 140718 ART-2025-140718 eng Alonso-Gutiérrez, David Universidad de Zaragoza (orcid)0000-0003-1256-3671 A general functional version of Grünbaum's inequality 2025 A classical inequality by Grünbaum provides a sharp lower bound for the ratio vol(K−)/vol(K), where K− denotes the intersection of a convex body with non-empty interior K ⊂ Rn with a halfspace bounded by a hyperplane H passing through the centroid g(K) of K. In this paper we extend this result to the case in which the hyperplane H passes by any of the points lying in a whole uniparametric family of r-powered centroids associated to K (depending on a real parameter r ≥ 0), by proving a more general functional result on concave functions. The latter result further connects (and allows one to recover) various inequalities involving the centroid, such as a classical inequality (due to Minkowski and Radon) that relates the distance of g(K) to a supporting hyperplane of K, or a result for volume sections of convex bodies proven independently by Makai Jr.&Martini and Fradelizi. Access copy available to the general public Unrestricted info:eu-repo/semantics/openAccess by-nc http://creativecommons.org/licenses/by-nc/3.0/es/ info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Marín Sola, Francisco Martín Goñi, Javier Yepes Nicolás, Jesús 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 544, 1 (2025), 129065 [20 pp.] J. math. anal. appl. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 0022-247X 399533 http://zaguan.unizar.es/record/146910/files/texto_completo.pdf Versión publicada 1754509 http://zaguan.unizar.es/record/146910/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:146910 articulos driver 2024-11-29-13:24:12 ARTICLE