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SL(n) covariant vector valuations on polytopes

Chunna Zeng Chongqing Normal University Dan Ma Shanghai Normal University

Convex and Discrete Geometry mathscidoc:1903.40001

Transactions of the American Mathematical Society, 370, (12), 8999–9023, 2018.12
All SL(n) covariant vector valuations on convex polytopes in R^n are completely classified without any continuity assumptions. The moment vector turns out to be the only such valuation if n ≥ 3, while two new functionals show up in dimension two.
moment vector, valuation, convex polytope, SL(n) covariance
[ Download ] [ 2019-03-20 13:12:42 uploaded by madan ] [ 759 downloads ] [ 0 comments ] 
@inproceedings{chunna2018sl(n),
  title={SL(n) covariant vector valuations on polytopes},
  author={Chunna Zeng, and Dan Ma},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190320131243178119216},
  booktitle={Transactions of the American Mathematical Society},
  volume={370},
  number={12},
  pages={8999–9023},
  year={2018},
}
Chunna Zeng, and Dan Ma. SL(n) covariant vector valuations on polytopes. 2018. Vol. 370. In Transactions of the American Mathematical Society. pp.8999–9023. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190320131243178119216.
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