Affine inequalities for Lp mean zonoids

Dongmeng Xi Shanghai University Lujun Guo Shanghai University Gangsong Leng Shanghai University

Convex and Discrete Geometry mathscidoc:1703.40036

Bulletin of the London Mathematical Society, 46, 367-378, 2014
In this paper, the Lp(p\geq1) mean zonoid of a convex body K is given, and we show that it is the Lp centroid body of radial (n+p)th mean body of K up to a dilation. We also establish some affine inequalities of these bodies by proving that the volume of the new bodies is decreasing under Steiner symmetrization.
Lp mean zonoids, Lp centroid bodies, affine inequalities, Steiner symmetrization.
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@inproceedings{dongmeng2014affine,
  title={Affine inequalities for Lp mean zonoids},
  author={Dongmeng Xi, Lujun Guo, and Gangsong Leng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170310210925065872652},
  booktitle={Bulletin of the London Mathematical Society},
  volume={46},
  pages={367-378},
  year={2014},
}
Dongmeng Xi, Lujun Guo, and Gangsong Leng. Affine inequalities for Lp mean zonoids. 2014. Vol. 46. In Bulletin of the London Mathematical Society. pp.367-378. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170310210925065872652.
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