TitleHigher codimension area-minimizing currents mod(q): structure of singularities near (m−1)-invariant cones
Publication TypeJournal Article
Year of Publication2024
AuthorsDe Lellis C, Minter P, Skorobogatova A
Type of ArticleInterior regularity

We study finer properties related to the interior regularity of m-dimensional area minimizing currents mod(q) in arbitrary codimension. We show that the set of points where at least one tangent cone is translation invariant along m-1 directions is locally a connected $C^{1,\beta}$ submanifold, and moreover such points have unique tangent cones. We establish these results as consequences of a fine excess decay theorem.