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Local Tensor Valuations

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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.

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Authors and Affiliations

  1. Department of Mathematics, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany

    Daniel Hug

  2. Mathematisches Institut, Albert-Ludwigs-Universität, 79104, Freiburg, Germany

    Rolf Schneider

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  1. Daniel Hug
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  2. Rolf Schneider
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Correspondence to Rolf Schneider.

Additional information

We acknowledge the support of the German Research Foundation (DFG) through the Research Unit ‘Geometry and Physics of Spatial Random Systems’ under the grant HU 1874/2-1.

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Hug, D., Schneider, R. Local Tensor Valuations. Geom. Funct. Anal. 24, 1516–1564 (2014). https://doi.org/10.1007/s00039-014-0289-0

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  • DOI: https://doi.org/10.1007/s00039-014-0289-0

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