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LYZ Matrices and SL($n$) Contravariant Valuations on Polytopes

Published online by Cambridge University Press:  18 December 2019

Dan Ma
Affiliation:
Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P.R.China, Email: madan@shnu.edu.cn
Wei Wang
Affiliation:
School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, 411201, P.R. China, Email: wwang@hnust.edu.cn
Corresponding

Abstract

All SL($n$) contravariant symmetric matrix valued valuations on convex polytopes in $\mathbb{R}^{n}$ are completely classified without any continuity assumptions. The general Lutwak–Yang–Zhang matrix is shown to be essentially the unique such valuation.

Type
Article
Copyright
© Canadian Mathematical Society 2019

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Footnotes

The work of the first author was supported in part by Shanghai Sailing Program (17YF1413800) and the National Natural Science Foundation of China (11701373). The work of the second author was supported in part by the Natural Science Foundation of Hunan Province (2017JJ3085 and 2019JJ50172).

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