SL($n$) contravariant tensor valuations of small orders
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913929261744128 |
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| author | Li, Jin Ma, Dan |
| author_facet | Li, Jin Ma, Dan |
| contents | A complete classification of \(\mathrm{SL}(n)\) contravariant, \(p\)-order tensor valuations on convex polytopes in \( \mathbb{R}^n \) for \( n \geq p \) is established without imposing additional assumptions, particularly omitting any symmetry requirements on the tensors. Beyond recovering known symmetric tensor valuations, our classification reveals asymmetric counterparts associated with the cross tensor and the Levi-Civita tensor. Additionally, some Minkowski type relations for these asymmetric tensor valuations are obtained, extending the classical Minkowski relation of surface area measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SL($n$) contravariant tensor valuations of small orders Li, Jin Ma, Dan Metric Geometry Functional Analysis 52B45, 52A20, 52B11 A complete classification of \(\mathrm{SL}(n)\) contravariant, \(p\)-order tensor valuations on convex polytopes in \( \mathbb{R}^n \) for \( n \geq p \) is established without imposing additional assumptions, particularly omitting any symmetry requirements on the tensors. Beyond recovering known symmetric tensor valuations, our classification reveals asymmetric counterparts associated with the cross tensor and the Levi-Civita tensor. Additionally, some Minkowski type relations for these asymmetric tensor valuations are obtained, extending the classical Minkowski relation of surface area measures. |
| title | SL($n$) contravariant tensor valuations of small orders |
| topic | Metric Geometry Functional Analysis 52B45, 52A20, 52B11 |
| url | https://arxiv.org/abs/2505.12277 |