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The minimal Orlicz surface area

Zou Du Wuhan University of Science and Technology Xiong Ge Tongji University

Convex and Discrete Geometry mathscidoc:1702.40009

Advances in Applied Mathematics, 61, (2), 25–45, 2014.8
Petty proved that a convex body in R^n has the minimal surface area amongst its SL(n)images, if, and only if, its surface area measure is isotropic. By introducing a new notion of minimal Orlicz surface area, we generalize this result to the Orlicz setting. The analog of Ball’s reverse isoperimetric inequality is established.
Minimal surface area; Reverse isoperimetric inequality; Orlicz Brunn–Minkowski theory
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  • http://dx.doi.org/10.1016/j.aam.2014.08.006
@inproceedings{zou2014the,
  title={The minimal Orlicz surface area},
  author={Zou Du, and Xiong Ge},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228130922425478567},
  booktitle={Advances in Applied Mathematics},
  volume={61},
  number={2},
  pages={25–45},
  year={2014},
}
Zou Du, and Xiong Ge. The minimal Orlicz surface area. 2014. Vol. 61. In Advances in Applied Mathematics. pp.25–45. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228130922425478567.
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