Work

SL(n) Contravariant Matrix-Valued Valuations on Polytopes

Year: 2024

Type: preprint

Abstract: All $\textrm{SL}(n)$ contravariant matrix-valued valuations on polytopes in $\mathbb{R}^n$ 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 $n\geq 4$, while a new function shows up in dimension three. In dimension two, the classification corresponds to the known case of $\textrm{SL}(2)$ equivariant matrix-valued valuations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2405.06897

Authors: Zeng, Chunna, Zhou, Yuqi

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G4952392286

OpenAlex ID: W4396913110

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