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arXiv · 2512.08375

A Characterization of Functional Affine Surface Areas

Fernanda M. Baêta
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Abstract

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.

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Fernanda M. Baêta. 2025-12-09. A Characterization of Functional Affine Surface Areas. https://arxiv.org/abs/2512.08375

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