The ratio between the volume of the p-centroid body of a convex body K in R-n and the volume of K attains its minimum value if and only if K is an origin symmetric ellipsoid. This result, the L-p-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 L-p-Busemann-Petty centroid inequality is a consequence of this general fact. (C) 2002 Elsevier Science (USA).

Campi, S., & Gronchi, P. (2002). The Lp-Busemann-Petty centroid inequality. ADVANCES IN MATHEMATICS, 167(1), 128-141 [10.1006/aima.2001.2036].

The Lp-Busemann-Petty centroid inequality

CAMPI, STEFANO;
2002

Abstract

The ratio between the volume of the p-centroid body of a convex body K in R-n and the volume of K attains its minimum value if and only if K is an origin symmetric ellipsoid. This result, the L-p-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 L-p-Busemann-Petty centroid inequality is a consequence of this general fact. (C) 2002 Elsevier Science (USA).
Campi, S., & Gronchi, P. (2002). The Lp-Busemann-Petty centroid inequality. ADVANCES IN MATHEMATICS, 167(1), 128-141 [10.1006/aima.2001.2036].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/17198
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