Title | Fine Structure of Singularities in Area-Minimizing Currents Mod(q) |
Publication Type | Journal Article |
Year of Publication | 2024 |
Authors | De Lellis C, Minter P, Skorobogatova A |
Type of Article | Interior regularity |
Abstract | We study fine structural properties related to the interior regularity of $m$-dimensional area minimizing currents mod$(q)$ in arbitrary codimension. We show: (i) 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; (ii) the remaining part of the singular set is countably $(m-2)$-rectifiable, with a unique flat tangent cone (with multiplicity) at $\mathcal{H}^{m-2}$-a.e. flat singular point. These results are consequences of fine excess decay theorems as well as almost monotonicity of a universal frequency function. |
Order:
17