Superforms, supercurrents and convex geometry
Metric Geometry
2025-01-30 v2 Algebraic Geometry
Complex Variables
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- Amp\`ere equations on the boundary of convex bodies.
Cite
@article{arxiv.2501.02896,
title = {Superforms, supercurrents and convex geometry},
author = {Bo Berndtsson},
journal= {arXiv preprint arXiv:2501.02896},
year = {2025}
}
Comments
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