2 citations · 3 across the 3 of their papers we have counts for
4 papers
Translation invariant valuations on quasi-concave functions
Andrea Colesanti, Nico Lombardi, Lukas Parapatits
We study real-valued, continuous and translation invariant valuations defined on the space of quasi-concave functions of N variables. In particular, we prove a homogeneous decompos…
A Valuation-Theoretic Approach to Translative-Equidecomposability
Katharina Kusejko, Lukas Parapatits
All simple translation-invariant valuations on polytopes are classified. As a direct consequence the well-known conditions for translative-equidecomposability are recovered. Furthe…
Moments and Valuations
Christoph Haberl, Lukas Parapatits
All measurable and -covariant vector valued valuations on convex polytopes containing the origin in their interiors are completely classified. The moment vect…
The Steiner Formula for Minkowski Valuations
Lukas Parapatits, Franz E. Schuster
A Steiner type formula for continuous translation invariant Minkowski valuations is established. In combination with a recent result on the symmetry of rigid motion invariant homog…