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arXiv · 2006.12933

Smooth valuations on convex functions

Jonas Knoerr
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Abstract

We construct valuations on the space of finite-valued convex functions using integration of differential forms over the differential cycle associated to a convex function. We describe the kernel of this procedure and show that the intersection of this space of smooth valuations with the space of all continuous dually epi-translation invariant valuations on convex functions is dense in the latter. As an application, we obtain a description of 1-homogeneous, continuous, dually epi-translation invariant valuations that are invariant with respect to a compact subgroup operating transitively on the unit sphere.

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Jonas Knoerr. 2020-06-23. Smooth valuations on convex functions. https://arxiv.org/abs/2006.12933

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