Preprint

Inserted: 22 mar 2024
Last Updated: 23 mar 2024

Year: 2024

Abstract:

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.

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• Mod_q_decay-2.pdf