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math.FA2024★ 1 cited
Inequalities and counterexamples for functional intrinsic volumes and beyond
Fabian Mussnig, Jacopo Ulivelli
We show that analytic analogs of Brunn-Minkowski-type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and…
math.FA2024
Polynomial valuations on convex functions and their maximal extensions
Jonas Knoerr, Jacopo Ulivelli
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extensi…