| 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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