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Approximation and characterization of generalised Lipschitz-Killing curvatures

✍ Scribed by M. Zähle

Publisher
Springer
Year
1990
Tongue
English
Weight
450 KB
Volume
8
Category
Article
ISSN
0232-704X

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✦ Synopsis

A differential-geometric and measure-geometric analogue to Hadwiger's characterization of linear combinations of Minkowski functionals of convex bodies as continuous additive euclidean invariants is given. The equivalent of the quermassintegrals are generalised Lipschitz-Killing curvatures and measures. By means of polyhedral approximation with respect to flat seminorms of associated normal cycles the general problem may be reduced to the classical case.

(Pk e -1 (Rd X Sd -) is the kth Lipschitz-Killing curvature form, k = 0, ... , d -1.

Ck(X, B) := N L B(p,), B e (Rd x Sd-1), is the kth (generalised) Lipschitz-Killing curvature measure of X.

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