Calculus of Variations and Geometric Measure Theory

C. De Lellis - P. Minter - A. Skorobogatova

Higher codimension area-minimizing currents mod$(q)$: structure of singularities near $(m-1)$-invariant cones

created by skorobogatova on 22 Mar 2024
modified on 23 Mar 2024



Inserted: 22 mar 2024
Last Updated: 23 mar 2024

Year: 2024


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.