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arXiv · 2301.10049

From valuations on convex bodies to convex functions

Jonas Knoerr·Jacopo Ulivelli
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Abstract

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.

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Jonas Knoerr, Jacopo Ulivelli. 2023-01-24. From valuations on convex bodies to convex functions. https://arxiv.org/abs/2301.10049

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