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.

On volume product inequalities for convex sets

CAMPI, STEFANO;
2006

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/21948
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