Title Regularity of area minimizing currents mod $p$ Publication Type Journal Article Year of Publication 2020 Authors De Lellis C., Hirsch J., Marchese A., Stuvard S. Journal Geom. Funct. Anal. Volume 30 Issue (5) Pagination 1224-1336 Type of Article Interior regularity Keywords area minimizing currents $\modp$, blow-up analysis, center manifold, Minimal surfaces, multiple valued functions, regularity theory Abstract We establish a first general partial regularity theorem for area minimizing currents $\modp$, 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 $\modp$ 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. Notes Geom. Funct. Anal., 30(5):1224-1336, 2020. URL https://link.springer.com/article/10.1007/s00039-020-00546-0
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