A characterization of functional affine surface areas
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.
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Banach Space Theory
Point processes and geometric inequalities
Publication details
- Journal / source
- Advances in Mathematics
- Volume
- 503
- Pages
- 111207–111207
- Publication date
- 19 August 2026
- Language
- EN