49 citations · 217 across the 14 of their papers we have counts for
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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…
The Hadwiger theorem on convex functions, IV: The Klain approach
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
New proofs of the Hadwiger theorem for smooth and for continuous valuations on convex functions are obtained, and the Klain-Schneider theorem on convex functions is established. In…
The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
A complete family of functional Steiner formulas is established. As applications, an explicit representation of functional intrinsic volumes using special mixed Monge-Ampère measur…
The Hadwiger theorem on convex functions, II: Cauchy-Kubota formulas
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
A new version of the Hadwiger theorem on convex functions is established and an explicit representation of functional intrinsic volumes is found using new functional Cauchy-Kubota…
The Hadwiger theorem on convex functions, I
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on is established. Th…
Minkowski valuations on convex functions
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
A classification of SL contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measur…
Valuations on Convex Functions
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
All continuous, SL and translation invariant valuations on the space of convex functions on are completely classified.