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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2405.06897 |
| Etiquetas: |
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- 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.