SL(n) Contravariant Matrix-Valued Valuations on Polytopes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913347774971904 |
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| author | Zeng, Chunna Zhou, Yuqi |
| author_facet | Zeng, Chunna Zhou, Yuqi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06897 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SL(n) Contravariant Matrix-Valued Valuations on Polytopes Zeng, Chunna Zhou, Yuqi Differential Geometry 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. |
| title | SL(n) Contravariant Matrix-Valued Valuations on Polytopes |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.06897 |