Curvature measures of convex bodies

Authors: Rolf Schneider

Publish Date: 1978/12/01

Volume: 116, Issue: 1, Pages: 101-134

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Abstract

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 are51 an integralgeometric 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 body61 an axiomatic characterization of the linear combinations of curvature measures similar to Hadwigers characterization of the quermassintegrals of convex bodies81 the determination of the support of the curvature measure of order m which turns out to be the closure of the mskeleton of the convex body Moreover we give for the case of convex bodies a new and comparatively short proof of an integralgeometric kinematic formula for curvature measures

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