Hard Lefschetz theorem for valuations and related questions of integral geometry
Abstract
Description
We study the properties of the multiplicative structure on valuations on convex sets. We prove a new version of the hard Lefschetz theorem for even translation invariant continuous valuations, and discuss related problems of integral geometry. Then we formulate a conjectural analogue of this result for odd valuations.
14 pages, revised version
14 pages, revised version