Premium
On the reverse L p –busemann–petty centroid inequality
Author(s) -
Campi Stefano,
Gronchi Paolo
Publication year - 2002
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300016004
Subject(s) - mathematics , centroid , convex body , combinatorics , chord (peer to peer) , affine transformation , maxima and minima , regular polygon , triangle inequality , invariant (physics) , mathematical analysis , convex hull , geometry , mathematical physics , distributed computing , computer science
The volume of the L p ‐centroid body of a convex body K ⊂ 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.