Hofstätter, G. C., & Knoerr, J. (2025). Equivariant valuations on convex functions. Calculus of Variations and Partial Differential Equations, 64, Article 242. https://doi.org/10.1007/s00526-025-03117-z
Calculus of Variations and Partial Differential Equations
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ISSN:
0944-2669
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Date (published):
8-Sep-2025
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Number of Pages:
16
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Publisher:
SPRINGER HEIDELBERG
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Peer reviewed:
Yes
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Keywords:
equivariant valuations; convex functions; projection body; difference body
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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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Project title:
Bewertungen auf konvexen Funktionen: P 34446-N (FWF - Österr. Wissenschaftsfonds)
