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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Polar duals of convex bodies


Author: Mostafa Ghandehari
Journal: Proc. Amer. Math. Soc. 113 (1991), 799-808
MSC: Primary 52A39
DOI: https://doi.org/10.1090/S0002-9939-1991-1057954-7
MathSciNet review: 1057954
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Abstract: A generalization and the dual version of the following result due to Firey is given: The mixed area of a plane convex body and its polar dual is at least $ \pi $. We give a sharp upper bound for the product of the dual cross-sectional measure of any index and that of its polar dual. A general result for a convex body $ K$ and a convex increasing real-valued function gives inequalities for sets of constant width and sets with equichordal points as special cases.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1057954-7
Keywords: Convex body, polar dual, mixed volume, dual mixed volume
Article copyright: © Copyright 1991 American Mathematical Society