35 citations · 86 across the 8 of their papers we have counts for
12 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…
Centro-Affine Tensor Valuations
Christoph Haberl, Lukas Parapatits
We completely classify all measurable -covariant symmetric tensor valuations on convex polytopes containing the origin in their interiors. It is shown that es…
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…
Log-Concavity Properties of Minkowski Valuations
Astrid Berg, Lukas Parapatits, Franz E. Schuster +1
New Orlicz Brunn-Minkowski inequalities are established for rigid motion compatible Minkowski valuations of arbitrary degree. These extend classical log-concavity properties of int…
Valuations and Surface Area Measures
Christoph Haberl, Lukas Parapatits
We consider valuations defined on polytopes containing the origin which have measures on the sphere as values. We show that the classical surface area measure is essentially the on…