# Regularity of area minimizing currents mod $p$

created by stuvard on 10 Sep 2019
modified on 12 Sep 2019

[BibTeX]

Preprint

Inserted: 10 sep 2019
Last Updated: 12 sep 2019

Year: 2019

ArXiv: 1909.05172 PDF

Abstract:

We establish a first general partial regularity theorem for area minimizing currents $\mathrm{mod}(p)$, for every $p$, in any dimension and codimension. More precisely, we prove that the Hausdorff dimension of the interior singular set of an $m$-dimensional area minimizing current $\mathrm{mod}(p)$ cannot be larger than $m-1$. Additionally, we show that, when $p$ is odd, the interior singular set is $(m-1)$-rectifiable with locally finite $(m-1)$-dimensional measure.