Annali di Matematica Pura ed Applicata

, Volume 116, Issue 1, pp 101–134

Curvature measures of convex bodies

  • Rolf Schneider

DOI: 10.1007/BF02413869

Cite this article as:
Schneider, R. Annali di Matematica (1978) 116: 101. doi:10.1007/BF02413869


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.

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1978

Authors and Affiliations

  • Rolf Schneider
    • 1
  1. 1.Freiburg i.Br.Germania Federale