Singular valuations and the Hadwiger theorem on convex functions
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910649626394624 |
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| author | Knoerr, Jonas |
| author_facet | Knoerr, Jonas |
| contents | We give a characterization of smooth, rotation and dually epi-translation invariant valuations and use this result to obtain a new proof of the Hadwiger theorem on convex functions. We also give a description of the construction of the functional intrinsic volumes using integration over the differential cycle and provide a new representation of these functionals as principal value integrals with respect to the Hessian measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05158 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Singular valuations and the Hadwiger theorem on convex functions Knoerr, Jonas Metric Geometry 52B45, 26B25, 53C65 We give a characterization of smooth, rotation and dually epi-translation invariant valuations and use this result to obtain a new proof of the Hadwiger theorem on convex functions. We also give a description of the construction of the functional intrinsic volumes using integration over the differential cycle and provide a new representation of these functionals as principal value integrals with respect to the Hessian measures. |
| title | Singular valuations and the Hadwiger theorem on convex functions |
| topic | Metric Geometry 52B45, 26B25, 53C65 |
| url | https://arxiv.org/abs/2209.05158 |