A Characterization of Functional Affine Surface Areas
Metric Geometry
2025-12-10 v1 Functional Analysis
Abstract
A characterization of valuations on the space of convex Lipschitz functions whose domain is a polytope in 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.
Cite
@article{arxiv.2512.08375,
title = {A Characterization of Functional Affine Surface Areas},
author = {Fernanda M. Baêta},
journal= {arXiv preprint arXiv:2512.08375},
year = {2025}
}