Dual Orlicz-Brunn-Minkowski theory

Baocheng Zhu Hubei University for Nationalities Jiazu Zhou Southwest University Wenxue Xu Southwest University

Convex and Discrete Geometry mathscidoc:1703.40040

In this paper, a dual Orlicz–Brunn–Minkowski theory is presented. An Orlicz radial sum and dual Orlicz mixed volumes are introduced. The dual Orlicz–Minkowski inequality and the dual Orlicz–Brunn–Minkowski inequality are estab-lished. The variational formula for the volume with respect to the Orlicz radial sum is proved. The equivalence between the dual Orlicz–Minkowski inequality and the dual Orlicz–Brunn–Minkowski inequality is demonstrated. Orlicz intersection bodies are defined and the Orlicz–Busemann–Petty problem is posed.
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@inproceedings{baochengdual,
  title={ Dual Orlicz-Brunn-Minkowski theory},
  author={Baocheng Zhu, Jiazu Zhou, and Wenxue Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170322012420235048725},
}
Baocheng Zhu, Jiazu Zhou, and Wenxue Xu. Dual Orlicz-Brunn-Minkowski theory. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170322012420235048725.
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