$\operatorname{SL}(n)$ contravariant function-valued valuations on polytopes
Metric Geometry
2026-03-13 v1 Functional Analysis
Abstract
We present a complete classification of contravariant, -valued valuations on polytopes, without any additional assumptions.It extends the previous results of the second author [Int. Math. Res. Not. 2020] which have a good connection with the and Orlicz Brunn-Minkowski theory. Additionally, our results deduce a complete classification of contravariant symmetric-tensor-valued valuations on polytopes.
Cite
@article{arxiv.2403.12890,
title = {$\operatorname{SL}(n)$ contravariant function-valued valuations on polytopes},
author = {Zhongwen Tang and Jin Li and Gangsong Leng},
journal= {arXiv preprint arXiv:2403.12890},
year = {2026}
}