Curvature measures and valuations

Wolfgang Weil (Karlsruhe)

The classical Steiner formula expresses the volume of an outer parallel set in terms of
additive functionals of different degree of homogeneity. For convex bodies, these 
functionals are the intrinsic volumes. A similar development is possible for more general 
additive functionals (valuations) and explicit formulas for a polynomial expansion are 
known in the case of convex polytopes. This raises the interesting question which 
continuous valuations on polytopes have a continuous extension to all convex bodies. For 
some partial answers, local variants of the intrinsic volumes, the curvature measures and 
their generalizations, play an important role.