Curvature measures of convex bodies |
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Authors: | Rolf Schneider |
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Institution: | (1) Freiburg i.Br., Germania Federale |
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Abstract: | 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.
Entrata in Redazione il 14 dicembre 1976. |
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