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On the reverse Lp–busemann–petty centroid inequality

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Stefano Campi  and
Paolo Gronchi
Stefano Campi
Affiliation:
Dipartimento di Matematica Pura e Applicata “G. Vitali”, Università degli Studi di Modena e Reggio Emilia, Via Campi 213 B, 41100 Modena, Italy. E-mail: campi@unimo.it
Paolo Gronchi
Affiliation:
Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Via Madonna del Piano- Edificio F, 50019 Sesto Fiorentino (FI), Italy. E-mail: paolo@fi.iac.cnr.it
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Abstract

The volume of the Lp-centroid body of a convex body K ⊂ ℝd 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 Lp-centroid body and related to classical open problems like the slicing problem. Some variants of the Lp-Busemann-Petty centroid inequality are established. The reverse form of these inequalities is proved in the two-dimensional case.

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 49 , Issue 1-2 , June 2002 , pp. 1 - 11
Copyright
Copyright © University College London 2002

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