Smooth valuations on convex functions
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Publication:6343540
DOI10.4310/JDG/1712344223arXiv2006.12933OpenAlexW3207957370MaRDI QIDQ6343540
Publication date: 23 June 2020
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.
Full work available at URL: https://doi.org/10.4310/jdg/1712344223
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