Lp minkowski valuations on polytopes

Jin Li Shanghai University Gangsong Leng Shanghai University

Convex and Discrete Geometry mathscidoc:1703.40034

Adv. Math., 299, 139-173, 2016
For $1 \leq p < \infty$, Ludwig, Haberl and Parapatits classified $L_p$ Minkowski valuations intertwining the special linear group with additional conditions such as homogeneity and continuity. In this paper,a complete classification of $L_p$ Minkowski valuations intertwining the special linear group on polytopes without any additional conditions is established for $p \geq 1$ including $p = \infty$. For $n=3$ and $p=1$, there exist valuations not mentioned before.
$L_\infty$ Minkowski valuation, $L_\infty$ projection body, $L_p$ Minkowski valuation, function-valued valuation, $\sln$ contravariant, $\sln$ covariant
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@inproceedings{jin2016lp,
  title={Lp MINKOWSKI VALUATIONS ON POLYTOPES},
  author={Jin Li, and Gangsong Leng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170310021513378225650},
  booktitle={Adv. Math.},
  volume={299},
  pages={139-173},
  year={2016},
}
Jin Li, and Gangsong Leng. Lp MINKOWSKI VALUATIONS ON POLYTOPES. 2016. Vol. 299. In Adv. Math.. pp.139-173. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170310021513378225650.
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