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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.

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  1. Friedrich-Schiller-Universität Jena, Sektion Mathematik Universitätsthochhaus, O-6900, Jena

    M. Zähle

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  1. M. Zähle
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Zähle, M. Approximation and characterization of generalised Lipschitz-Killing curvatures. Ann Glob Anal Geom 8, 249–260 (1990). https://doi.org/10.1007/BF00127938

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  • DOI: https://doi.org/10.1007/BF00127938

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