A Characterization of Functional Affine Surface Areas
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918239206899712 |
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| author | Baêta, Fernanda M. |
| author_facet | Baêta, Fernanda M. |
| contents | A characterization of valuations on the space of convex Lipschitz functions whose domain is a polytope in $\mathbb{R}^n$ is obtained. It is shown that every upper semicontinuous, equi-affine and dually epi-translation invariant valuation can be written as a linear combination of a constant term, the volume of the domain, and a functional affine surface area. In addition, dual statements for finite-valued convex functions are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Characterization of Functional Affine Surface Areas Baêta, Fernanda M. Metric Geometry Functional Analysis A characterization of valuations on the space of convex Lipschitz functions whose domain is a polytope in $\mathbb{R}^n$ is obtained. It is shown that every upper semicontinuous, equi-affine and dually epi-translation invariant valuation can be written as a linear combination of a constant term, the volume of the domain, and a functional affine surface area. In addition, dual statements for finite-valued convex functions are established. |
| title | A Characterization of Functional Affine Surface Areas |
| topic | Metric Geometry Functional Analysis |
| url | https://arxiv.org/abs/2512.08375 |