Annals of Global Analysis and Geometry

, Volume 8, Issue 3, pp 249–260

Approximation and characterization of generalised Lipschitz-Killing curvatures

  • M. Zähle

DOI: 10.1007/BF00127938

Cite this article as:
Zähle, M. Ann Glob Anal Geom (1990) 8: 249. doi:10.1007/BF00127938


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.

Copyright information

© Deutscher Verlag der Wissenschaften 1990

Authors and Affiliations

  • M. Zähle
    • 1
  1. 1.Friedrich-Schiller-Universität JenaSektion Mathematik UniversitätsthochhausJena