3 papers
math.MG2024
The Klain approach to zonal valuations
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
We show an analogue of the Klain-Schneider theorem for valuations that are invariant under rotations around a fixed axis, called zonal. Using this, we establish a new integral repr…
math.MG2024
Lefschetz operators on convex valuations
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
We investigate the action of Alesker's Lefschetz operators on translation invariant valuations on convex bodies. For scalar valued valuations, we describe this action on the level…
math.MG2023
Fixed Points of Mean Section Operators
Leo Brauner, Oscar Ortega-Moreno
We characterize rotation equivariant bounded linear operators from to by the mass distribution of the spherical Laplacian of their ker…