The L-busemann-petty Centroid Inequality
نویسندگان
چکیده
The ratio between the volume of the p-centroid body of a convex body K in Rn and the volume of K attains its minimum value if and only if K is an origin symmetric ellipsoid. This result, the Lp-Busemann-Petty centroid inequality, was recently proved by Lutwak, Yang and Zhang. In this paper we show that all the intrinsic volumes of the p-centroid body of K are convex functions of a time-like parameter when K is moved by shifting all the chords parallel to a fixed direction. The Lp-Busemann-Petty centroid inequality is a consequence of this general fact.
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