Centro-Affine Tensor Valuations
Abstract
We completely classify all measurable $\operatorname{SL}(n)$-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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2015
- DOI:
- 10.48550/arXiv.1509.03831
- arXiv:
- arXiv:1509.03831
- Bibcode:
- 2015arXiv150903831H
- Keywords:
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- Mathematics - Metric Geometry;
- 52B45;
- 52A20