The volume of the polar body of a symmetric convex set K of Rd 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-Santalo' inequality for two-dimensional convex sets.
On volume product inequalities for convex sets / S. CAMPI; P. GRONCHI. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 134:(2006), pp. 2393-2402. [10.1090/S0002-9939-06-08241-4]
On volume product inequalities for convex sets
GRONCHI, PAOLO
2006
Abstract
The volume of the polar body of a symmetric convex set K of Rd 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-Santalo' inequality for two-dimensional convex sets.
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