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De Lellis, Camillo; Spadaro, Emanuele; Spolaor, Luca (2018). Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation. Transactions of the American Mathematical Society, 370(3):1783-1801.
We construct Lipschitz Q-valued functions which carefully approximate integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the discreteness of the singular set for the following three classes of 2-dimensional integral currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of 3-dimensional area minimizing cones.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics |
| Language: | English |
| Date: | 2018 |
| Deposited On: | 07 Mar 2018 16:33 |
| Last Modified: | 18 Jan 2025 02:38 |
| Publisher: | American Mathematical Society |
| ISSN: | 0002-9947 |
| OA Status: | Hybrid |
| Free access at: | Publisher DOI. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.1090/tran/6995 |
| Project Information: |
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De Lellis, Camillo