The Vectorial Hadwiger Theorem on Convex Functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912342689710080 |
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| author | Mouamine, Mohamed A. Mussnig, Fabian |
| author_facet | Mouamine, Mohamed A. Mussnig, Fabian |
| contents | A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally extend the classical Minkowski relations. For this, the existence of these operators with singular densities is shown, along with additional representations involving mixed Monge-Ampère measures, Kubota-type formulas, and area measures of higher dimensional convex bodies. Dual results are formulated for valuations on super-coercive convex functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Vectorial Hadwiger Theorem on Convex Functions Mouamine, Mohamed A. Mussnig, Fabian Metric Geometry Functional Analysis 52B45 (Primary) 26B12, 26B15, 26B25, 52A39, 52A41 (Secondary) A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally extend the classical Minkowski relations. For this, the existence of these operators with singular densities is shown, along with additional representations involving mixed Monge-Ampère measures, Kubota-type formulas, and area measures of higher dimensional convex bodies. Dual results are formulated for valuations on super-coercive convex functions. |
| title | The Vectorial Hadwiger Theorem on Convex Functions |
| topic | Metric Geometry Functional Analysis 52B45 (Primary) 26B12, 26B15, 26B25, 52A39, 52A41 (Secondary) |
| url | https://arxiv.org/abs/2504.04952 |