SL(n) contravariant function-valued valuations on polytopes

2024/03/19 by Tang, Zhongwen, Li, Jin, Leng, Gangsong · 1 citation
#52A39 #52B11 #52B45 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2403.12890

Abstract

We present a complete classification of SL(n) contravariant, C(ℝⁿ∖\o\)-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 L_p and Orlicz Brunn-Minkowski theory. Additionally, our results deduce a complete classification of SL(n) contravariant symmetric-tensor-valued valuations on polytopes.

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