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General Affine Invariances Related to Mahler Volume

Dongmeng Xi Shanghai University Yiming Zhao Massachusetts Institute of Technology

Convex and Discrete Geometry mathscidoc:2112.40003

International Mathematics Research Notices, 2021.4
General affine invariances related to Mahler volume are introduced. We establish their affine isoperimetric inequalities by using a symmetrization scheme that involves a total of 2n elaborately chosen Steiner symmetrizations at a time. The necessity of this scheme, as opposed to the usual Steiner symmetrization, is demonstrated with an example (see the Appendix).
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@inproceedings{dongmeng2021general,
  title={General Affine Invariances Related to Mahler Volume},
  author={Dongmeng Xi, and Yiming Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20211226210747754366890},
  booktitle={International Mathematics Research Notices},
  year={2021},
}
Dongmeng Xi, and Yiming Zhao. General Affine Invariances Related to Mahler Volume. 2021. In International Mathematics Research Notices. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20211226210747754366890.
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