School of Mathematical Sciences

Department Colloquium

Schreiber 006, 12:15

University of Freiburg

One of the best known theorems of classical convex geometry is Hadwiger's characterization

Abstract:

theorem. It says that any continuous motion invariant real valuation on the space of convex bodies in

$n$-dimensional Euclidean space is a linear combination of the intrinsic volumes. The latter arise as

coefficients in the Steiner polynomial for the volume of a parallel body. This approach has been generalized

in different ways: local parallel sets lead to curvature measures, replacement of the volume by higher order

moments leads to tensor valuations. In both cases, analogues of Hadwiger's characterization theorem have

been proved. The subject of the talk is a common generalization. We give a complete classification of tensor

measure valued valuations on convex bodies with some basis properties, like isometry covariance and weak

continuity. (This is joint work with Daniel Hug.)

Coffee will be served at 12:00 before the lecture

at Schreiber building 006