TitleArea minimizing currents mod $2Q$: linear regularity theory
Publication TypeJournal Article
AuthorsDe Lellis C., Hirsch J., Marchese A., Stuvard S.
Type of ArticleQ-valued
Keywordsarea minimizing currents $\modp$, Dirichlet integral, linearization., Minimal surfaces, multiple valued functions, regularity theory

We establish a theory of $Q$-valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents $\modp$ when $p=2Q$, and to establish a first general partial regularity theorem for every $p$ in any dimension and codimension.


To appear in Communications on Pure and Applied Mathematics