Hard Lefschetz theorem for valuations and related questions of integral geometry

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121931We 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 versionMetric GeometryDifferential GeometryHard Lefschetz theorem for valuations and related questions of integral geometrytext