SL($\textbf {\textit {n}}$) covariant vector valuations on polytopes
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- by Chunna Zeng and Dan Ma PDF
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Abstract:
All $\mathrm {SL}(n)$ covariant vector valuations on convex polytopes in $\mathbb {R}^n$ are completely classified without any continuity assumptions. The moment vector turns out to be the only such valuation if $n\ge 3$, while two new functionals show up in dimension two.References
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Additional Information
- Chunna Zeng
- Affiliation: School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, People’s Republic of China; and Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8–10/1046, 1040 Wien, Austria
- MR Author ID: 878564
- Email: zengchn@163.com
- Dan Ma
- Affiliation: Department of Mathematics, Shanghai Normal University, Shanghai 200234, People’s Republic of China
- MR Author ID: 1006081
- Email: madan@shnu.edu.cn
- Received by editor(s): April 25, 2017
- Received by editor(s) in revised form: November 20, 2017
- Published electronically: August 17, 2018
- Additional Notes: The first author was supported in part by the National Natural Science Foundation of China (Project No. 11801048), by the Chinese Scholarship Council and by the Natural Science Foundation Project of CSTC (Grant No. cstc2017jcyjAX0022).
The second author was supported in part by Shanghai Sailing Program 17YF1413800 and by the National Natural Science Foundation of China (Project No. 11701373). The second author is the corresponding author. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 8999-9023
- MSC (2010): Primary 52B45, 52A20
- DOI: https://doi.org/10.1090/tran/7468
- MathSciNet review: 3864403