Knörr, J., & Ulivelli, J. (2024). From valuations on convex bodies to convex functions. Mathematische Annalen, 390(4), 5987–6011. https://doi.org/10.1007/s00208-024-02902-z
A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by McMullen can be used to obtain a characterization of continuous, epi-translation invariant, and n-epi-homogeneous valuations on convex functions, which was previously established by Colesanti, Ludwig, and Mussnig. Following an approach by Goodey and Weil, a new characterization of 1-epi-homogeneous valuations is obtained.
