Publication date:
20 August 2017
Source:Advances in Mathematics, Volume 316
Author(s): Christoph Haberl, Lukas Parapatits
All measurable $\mathrm{SL}(n)$-covariant symmetric tensor valuations on convex polytopes containing the origin in their interiors are completely classified. It is shown that essentially the only examples of such valuations are the moment tensor and a tensor derived from $L_p$ surface area measures. This generalizes and unifies earlier results for the scalar, vector and matrix valued case.