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Volume inequalities for the i-th-convolution bodies

 

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Author: Alonso Gutiérrez, David
González Merino, Bernardo
Jiménez Gómez, Carlos Hugo
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2015-04-01
Published in: Journal of Mathematical Analysis and Applications, 424 (1), 385-401.
Document type: Article
Abstract: We obtain a new extension of Rogers-Sephard 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.
Cite: Alonso Gutiérrez, D., González Merino, B. y Jiménez Gómez, C.H. (2015). Volume inequalities for the i-th-convolution bodies. Journal of Mathematical Analysis and Applications, 424 (1), 385-401.
Size: 206.1Kb
Format: PDF

URI: http://hdl.handle.net/11441/46756

DOI: 10.1016/j.jmaa.2014.11.033

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