24 citations · 41 across the 6 of their papers we have counts for
6 papers
Generalized outer linearizations and extremal properties of rotational epi-symmetrizations
Steven Hoehner, Fabian Mussnig
We develop a functional extension of an extremal principle by Schneider (Monatsh. Math., 1967) by introducing generalized outer linearizations of convex functions. Given a coercive…
The Vectorial Hadwiger Theorem on Convex Functions
Mohamed A. Mouamine, Fabian Mussnig
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently i…
A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions
Mohamed A. Mouamine, Fabian Mussnig
A functional analog of the Klain-Schneider theorem for vector-valued valuations on convex functions is established, providing a classification of continuous, translation covariant,…
Metrics and Isometries for Convex Functions
Ben Li, Fabian Mussnig
We introduce a class of functional analogs of the symmetric difference metric on the space of coercive convex functions on with full-dimensional domain. We show that…
invariant valuations on super-coercive convex functions
Fabian Mussnig
All non-negative, continuous, and translation invariant valuations on the space of super-coercive, convex functions on are classified. Further…
Volume, Polar Volume and Euler Characteristic for Convex Functions
Fabian Mussnig
Functional analogs of the Euler characteristic and volume together with a new analog of the polar volume are characterized as non-negative, continuous, and t…