Volume inequalities for the i-th-convolution bodies
Scholar | Other documents of the author: Alonso Gutiérrez, David; González, Bernardo; Jimenez, C. Hugo
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TitleVolume inequalities for the i-th-convolution bodies
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. [-]
Bibliographic citationALONSO-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.
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