Open Access
February 2010 Orlicz centroid bodies
Erwin Lutwak, Deane Yang, Gaoyong Zhang
J. Differential Geom. 84(2): 365-387 (February 2010). DOI: 10.4310/jdg/1274707317


The sharp affine isoperimetric inequality that bounds the volume of the centroid body of a star body (from below) by the volume of the star body itself is the Busemann-Petty centroid inequality. A decade ago, the $L_p$ analogue of the classical Busemann- Petty centroid inequality was proved. Here, the definition of the centroid body is extended to an Orlicz centroid body of a star body, and the corresponding analogue of the Busemann-Petty centroid inequality is established for convex bodies.


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Erwin Lutwak. Deane Yang. Gaoyong Zhang. "Orlicz centroid bodies." J. Differential Geom. 84 (2) 365 - 387, February 2010.


Published: February 2010
First available in Project Euclid: 24 May 2010

zbMATH: 1206.49050
MathSciNet: MR2629512
Digital Object Identifier: 10.4310/jdg/1274707317

Rights: Copyright © 2010 Lehigh University

Vol.84 • No. 2 • February 2010
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