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Inequalities for dual isoperimetric deficits
Author(s) -
Gardner R. J.,
Vassallo S.
Publication year - 1998
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014200
Subject(s) - isoperimetric inequality , mathematics , dual (grammatical number) , mixed volume , convex body , ball (mathematics) , inequality , minkowski space , star (game theory) , regular polygon , pure mathematics , combinatorics , mathematical analysis , convex hull , geometry , art , literature
We study dual isoperimetric deficits of star bodies. We introduce the dual Steiner ball of a star body, and use it to establish an inequality for the L p distance, p = 2 and p = ∞, between the radial functions of two convex bodies. By applying this inequality, we find dual Bonnesen‐type inequalities for convex bodies. Finally, we use a general form of Grüss's inequality to derive dual Favard‐type inequalities for star and convex bodies. The results contribute to the dual Brunn–Minkowski theory initiated by E. Lutwak, and continue the attempt to understand the relation between this and the classical Brunn–Minkowski theory.