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arXiv · 2407.08304

Equivariant Valuations on Convex Functions

Georg C. Hofstätter·Jonas Knoerr
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Abstract

We classify all continuous valuations on the space of finite convex functions with values in the same space which are dually epi-translation-invariant and equi- resp. contravariant with respect to volume-preserving linear maps. We thereby identify the valuation-theoretic functional analogues of the difference body map and show that there does not exist a generalization of the projection body map in this setting. This non-existence result is shown to also hold true for valuations with values in the space of convex functions that are finite in a neighborhood of the origin.

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Georg C. Hofstätter, Jonas Knoerr. 2024-07-11. Equivariant Valuations on Convex Functions. https://arxiv.org/abs/2407.08304

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