Polar DuaLs of Convex Bodies
Technical rept. Jul-Sep 1989
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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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 Kappa and a convex increasing real valued function gives inequalities for sets of constant width and sets with equichordal points as special cases. Keywords Polar duals Convex bodies.
- Theoretical Mathematics