Polar duals of convex bodies
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- by Mostafa Ghandehari PDF
- Proc. Amer. Math. Soc. 113 (1991), 799-808 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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