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Monatshefte für Mathematik

, Volume 171, Issue 3–4, pp 459–479 | Cite as

Local tensor valuations on convex polytopes

  • Rolf Schneider
Article

Abstract

Local versions of the Minkowski tensors of convex bodies in \(n\)-dimensional Euclidean space are introduced. An extension of Hadwiger’s characterization theorem for the intrinsic volumes, due to Alesker, states that the continuous, isometry covariant valuations on the space of convex bodies with values in the vector space of symmetric \(p\)-tensors are linear combinations of modified Minkowski tensors. We ask for a local analogue of this characterization, and we prove a classification result for local tensor valuations on polytopes, without a continuity assumption.

Keywords

Tensor valuation Minkowski tensor Convex polytope Isometry covariance Characterization theorem 

Mathematics Subject Classification (2000)

MSC 52A20 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Mathematisches InstitutFreiburg i. Br.Germany

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