The volume of the polar body of a symmetric convex set K of R^d is investigated. It is shown that its reciprocal is a convex function of the time t along movements, in which every point of K moves with constant speed parallel to a fixed direction. This result is applied to find reverse forms of the Lp-Blaschke-Santalò inequality for two-dimensional convex sets.
Campi, S., Gronchi, P. (2006). On volume product inequalities for convex sets. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134(8), 2393-2402 [10.1090/S0002-9939-06-08241-4].
On volume product inequalities for convex sets
CAMPI S.;
2006-01-01
Abstract
The volume of the polar body of a symmetric convex set K of R^d is investigated. It is shown that its reciprocal is a convex function of the time t along movements, in which every point of K moves with constant speed parallel to a fixed direction. This result is applied to find reverse forms of the Lp-Blaschke-Santalò inequality for two-dimensional convex sets.
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https://hdl.handle.net/11365/21948
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