Orlicz centroid bodies

Erwin Lutwak Polytechnic Institute of NYU Deane Yang Polytechnic Institute of NYU Gaoyong Zhang Polytechnic Institute of NYU

Differential Geometry mathscidoc:1609.10165

Journal of Differential Geometry, 84, (2), 365-387, 2010
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 Lp analogue of the classical BusemannPetty 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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  author={Erwin Lutwak, Deane Yang, and Gaoyong Zhang},
  booktitle={Journal of Differential Geometry},
Erwin Lutwak, Deane Yang, and Gaoyong Zhang. ORLICZ CENTROID BODIES . 2010. Vol. 84. In Journal of Differential Geometry. pp.365-387. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911212338774304822.
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