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Geometric and Functional Analysis

, Volume 24, Issue 5, pp 1516–1564 | Cite as

Local Tensor Valuations

  • Daniel Hug
  • Rolf Schneider
Article

Abstract

The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant Minkowski tensors that were introduced by McMullen and characterized by Alesker. In analogy to the characterization theorems of Hadwiger and Alesker, we give here a complete classification of all locally defined tensor measures on convex bodies that share with the local Minkowski tensors the basic geometric properties of isometry covariance and weak continuity.

Keywords and phrases

Valuation Minkowski tensor Tensor valuation Support measure Characterization theorem Weak continuity Normal cycle 

Mathematics Subject Classification (2010)

Primary 52A20 Secondary 52A22 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Mathematisches InstitutAlbert-Ludwigs-UniversitätFreiburgGermany

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