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Inequalities for dual isoperimetric deficits

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

R. J. Gardner  and
S. Vassallo
R. J. Gardner
Affiliation:
Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063, U.S.A. e-mail: gardner@baker.math.wwu.edu
S. Vassallo
Affiliation:
Universitá Cattolica del S. Cuore, Largo Gemelli 1, 1-20123 Milan, Italy. e-mail: vassallo@mi.unicatt.it
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Abstracat

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 Lp 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.

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 45 , Issue 2 , December 1998 , pp. 269 - 285
Copyright
Copyright © University College London 1998

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