https://neckpinch.com/authors/bo-berndtsson/New arXiv papers by Bo Berndtsson, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1805.00379/arxiv:1805.00379Tue, 01 May 2018 00:00:00 GMTBo Berndtsson — Supercurrents, as introduced by Lagerberg, were mainly motivated as a way to study tropical varieties. Here we will associate a supercurrent to any smooth submanifold of Rⁿ. Positive supercurrents resemble positive currents in complex analysis, but depend on a choice of scalar product on Rⁿ and reflect the induced Riemannian structure on the submanifold. In this way we can use techniques from complex analysis to study real submanifolds. We illustrate the idea by giving area estimates of minimal manifolds and a monotinicity property of the mean curvature flow. We also illustrate the idea by a relatively short proof of Weyl's tube formula.Mean curvature flow