Sharp affine isoperimetric inequalities for the volume decomposition functionals of polytopes

Liu Yude Tongji University Sun Qiang Tongji University Xiong Ge Tongji University

Convex and Discrete Geometry mathscidoc:2108.40001

Advances in Mathematics, 389, 107902, 2021.8
The nth power of the volume functional Vnof polytopes P in R^n, according to dimensions of the spaces spanned by any nunit outer normal vectors of P, is decomposed into nhomogeneous polynomials of degree n. A set of new sharp affine isoperimetric inequalities for these volume decomposition functionals in R^3 are established, which essentially characterize the geometric and algebraic structures of polytopes.
Polytope; volume decomposition functional; affine isoperimetric inequality
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@inproceedings{liu2021sharp,
  title={Sharp affine isoperimetric inequalities for the volume decomposition functionals of polytopes},
  author={Liu Yude, Sun Qiang, and Xiong Ge},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210810120147750071852},
  booktitle={Advances in Mathematics},
  volume={389},
  pages={107902},
  year={2021},
}
Liu Yude, Sun Qiang, and Xiong Ge. Sharp affine isoperimetric inequalities for the volume decomposition functionals of polytopes. 2021. Vol. 389. In Advances in Mathematics. pp.107902. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210810120147750071852.
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