, Volume 8, Issue 3, pp 249-260

Approximation and characterization of generalised Lipschitz-Killing curvatures

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Abstract

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.