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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 116, Issue 1, pp 101–134 | Cite as

Curvature measures of convex bodies

  • Rolf Schneider
Article

Summary

The curvature measures, introduced by Federer for the sets of positive reach, are investigated in the special case of convex bodies. This restriction yields additional results. Among them are:(5.1), an integral-geometric interpretation of the curvature measure of order m, showing that it measures, in a certain sense, the affine subspaces of codimension m+1 which touch the convex body;(6.1), an axiomatic characterization of the (linear combinations of) curvature measures similar to Hadwiger's characterization of the quermassintegrals of convex bodies;(8.1), the determination of the support of the curvature measure of order m, which turns out to be the closure of the m-skeleton of the convex body. Moreover we give, for the case of convex bodies, a new and comparatively short proof of an integral-geometric kinematic formula for curvature measures.

Keywords

Linear Combination Convex Body Additional Result Short Proof Curvature Measure 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata (1923 -) 1978

Authors and Affiliations

  • Rolf Schneider
    • 1
  1. 1.Freiburg i.Br.Germany

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