Volume inequalitites for the i-th convolution bodies

Alonso Gutiérrez, David; González, Bernardo; Jiménez, Carlos Hugo

doi:10.1016/j.jmaa.2014.11.033

Volume inequalitites for the i-th convolution bodies

Alonso Gutiérrez, David (Universidad de Zaragoza) ; González, Bernardo ; Jiménez, Carlos Hugo

Resumen: We obtain a new extension of Rogers–Shephard inequality providing an upper bound for the volume of the sum of two convex bodies K and L. We also give lower bounds for the volume of the k-th limiting convolution body of two convex bodies K and L. Special attention is paid to the (n - 1)-th limiting convolution body, for which a sharp inequality, which is equality only when K = -L is a simplex, is given. Since the n-th limiting convolution body of K and -K is the polar projection body of K, these inequalities can be viewed as an extension of Zhang’s inequality.
Idioma: Inglés
DOI: 10.1016/j.jmaa.2014.11.033
Año: 2015
Publicado en: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 424 (2015), 385-401
ISSN: 0022-247X
Factor impacto JCR: 1.014 (2015)
Categ. JCR: MATHEMATICS rank: 56 / 311 = 0.18 (2015) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 88 / 254 = 0.346 (2015) - Q2 - T2
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2009-10418
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2010-16679
Tipo y forma: Article (PrePrint)
Área (Departamento): Análisis Matemático (Departamento de Matemáticas)
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Volume inequalitites for the i-th convolution bodies