Centro-Affine Tensor Valuations

Abstract

We completely classify all measurable $\mathrm{SL}(n)$-covariant symmetric tensor valuations on convex polytopes containing the origin in their interiors. 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.