2024/05/11 by Chunna Zeng, Yuqi Zhou, Zeng, Chunna +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2405.06897
openalex publication_date 2024/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
All \textrmSL(n) contravariant matrix-valued valuations on polytopes in ℝn are completely classified without any continuity assumptions. Moreover, the symmetry assumption of matrices is removed. The general Lutwak-Yang-Zhang matrix turns out to be the only such valuation if n≥ 4, while a new function shows up in dimension three. In dimension two, the classification corresponds to the known case of \textrmSL(2) equivariant matrix-valued valuations.