The volume of the L-p-centroid body of a convex body K subset of R-d is a convex function of a time-like parameter when each chord of K parallel to a fixed direction moves with constant speed. This fact is used to study extrema of some affine invariant functionals involving the volume of the L-p-centroid body and related to classical open problems like the slicing problem. Some variants of the L-p-Busemann-Petty centroid inequality are established. The reverse form of these inequalities is proved in the two-dimensional case.

Campi, S., & Gronchi, P. (2002). On the reverse Lp-Busemann-Petty centroid inequality. MATHEMATIKA, 49(97-98), 1-11 [10.1112/S0025579300016004].

On the reverse Lp-Busemann-Petty centroid inequality

CAMPI, STEFANO;
2002

Abstract

The volume of the L-p-centroid body of a convex body K subset of R-d is a convex function of a time-like parameter when each chord of K parallel to a fixed direction moves with constant speed. This fact is used to study extrema of some affine invariant functionals involving the volume of the L-p-centroid body and related to classical open problems like the slicing problem. Some variants of the L-p-Busemann-Petty centroid inequality are established. The reverse form of these inequalities is proved in the two-dimensional case.
Campi, S., & Gronchi, P. (2002). On the reverse Lp-Busemann-Petty centroid inequality. MATHEMATIKA, 49(97-98), 1-11 [10.1112/S0025579300016004].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/6815
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