The mixed Lp geominimal surface areas for multiple convex bodies

Deping Ye Memorial University of Newfoundland Baocheng Zhu Hubei University for Nationalities Jiazu Zhou Southwest University

Convex and Discrete Geometry mathscidoc:1703.40039

In this paper, we introduce several mixed Lp geominimal surface areas for multiple convex bodies for all $−n\neq p \in R$. Our definitions are motivated from an equivalent formula for the mixed p-affine surface area. Some properties, such as the affine invariance, for these mixed Lp geominimal surface areas are proved. Related inequalities, such as, Alexander-Fenchel type inequality, Santal´o style inequality, affine isoperimetric inequalities, and cyclic inequalities are established. Moreover, we also study some properties and inequalities for the i-th mixed Lp geominimal surface areas for two convex bodies.
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@inproceedings{depingthe,
  title={The mixed Lp geominimal surface areas for multiple convex bodies},
  author={Deping Ye, Baocheng Zhu, and Jiazu Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170322012209016802724},
}
Deping Ye, Baocheng Zhu, and Jiazu Zhou. The mixed Lp geominimal surface areas for multiple convex bodies. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170322012209016802724.
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