Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, June 03, 2013

Schreiber 006, 12:15

Rolf Schneider

University of Freiburg

Tensor valuations on convex bodies

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