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De Lellis, Camillo; Hirsch, Jonas; Marchese, Andrea; Stuvard, Salvatore (2020). Regularity of area minimizing currents mod p. Geometric and Functional Analysis, 30(5):1224-1336.
We establish a first general partial regularity theorem for area minimizing currents 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 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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 340 Law
610 Medicine & health 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Analysis
Physical Sciences > Geometry and Topology |
| Uncontrolled Keywords: | Geometry and Topology, Analysis |
| Language: | English |
| Date: | 1 October 2020 |
| Deposited On: | 17 Dec 2020 06:39 |
| Last Modified: | 24 Dec 2024 02:38 |
| Publisher: | Springer |
| ISSN: | 1016-443X |
| OA Status: | Hybrid |
| Free access at: | Publisher DOI. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.1007/s00039-020-00546-0 |
De Lellis, Camillo