A general functional version of Grünbaum's inequality
Alonso-Gutiérrez, David (Universidad de Zaragoza) ; Marín Sola, Francisco ; Martín Goñi, Javier ; Yepes Nicolás, Jesús
Resumen: 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.
Idioma: Inglés
DOI: 10.1016/j.jmaa.2024.129065
Año: 2025
Publicado en: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 544, 1 (2025), 129065 [20 pp.]
ISSN: 0022-247X
Tipo y forma: Article (Published version)
Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes.
Exportado de SIDERAL (2024-11-29-13:24:12)
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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.
Idioma: Inglés
DOI: 10.1016/j.jmaa.2024.129065
Año: 2025
Publicado en: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 544, 1 (2025), 129065 [20 pp.]
ISSN: 0022-247X
Tipo y forma: Article (Published version)
Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. Exportado de SIDERAL (2024-11-29-13:24:12)
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Record created 2024-11-29, last modified 2024-11-29