Christoph Haberl

Minkowski valuations intertwining the special linear group

All continuous Minkowski valuations which are compatible with the special linear group are completely classi?ed. One consequence of these classi?cations is a new characterization of the projection body operator.

The Centro-Affine Hadwiger Theorem

All upper semicontinuous and SL(n) invariant valuations on convex bodies containing the origin in their interiors are completely classified. Each such valuation is shown to be a linear combination of the Euler characteristic, the volume, the volume of the polar body, and the recently discovered Orlicz surface areas.

Moments and valuations

All measurable and

General

{\rm SL}(n)

L_p

-covariant vector valued valuations on convex polytopes containing the origin in their interiors are completely classified. The moment vector is shown to be essentially the only such valuation.