Superforms, supercurrents and convex geometry
arXiv:2501.02896
Abstract
We develop the calculus of superforms as a tool for convex geometry. The formalism is applied to valuations on convex bodies, the Alexandrov-Fenchel inequalities and Monge- Ampère equations on the boundary of convex bodies.
66 pages. In the first revision we correct (quite) a few misprints. A dubious remark on page 53 is deleted following a comment by Ramon van Handel The new revision is hopefully better organized than the previous one, although longer (93 pages)