Volume inequalities for the i-th-convolution bodies
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Other documents of the author: Alonso Gutiérrez, David; González, Bernardo; Jimenez, C. Hugo
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
Volume inequalities for the i-th-convolution bodiesDate
2015-04Publisher
ElsevierBibliographic citation
ALONSO-GUTIÉRREZ, David; GONZÁLEZ, Bernardo; JIMÉNEZ, Carlos Hugo. Volume inequalities for the i-th-convolution bodies. Journal of Mathematical Analysis and Applications, 2015, vol. 424, no 1, p. 385-401.Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0022247X14010646Version
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Abstract
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 ... [+]
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)(n−1)-th limiting convolution body, for which a sharp inequality, which is equality only when K=−LK=−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. [-]
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Journal of Mathematical Analysis and Applications Volume 424, Issue 1, 1 April 2015Rights
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