Calculus of Variations and Geometric Measure Theory

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

The fine structure of the singular set of area-minimizing integral currents III: Frequency 1 flat singular points and $\mathcal{H}^{m-2}$-a.e. uniqueness of tangent cones

created by delellis on 23 Apr 2023
modified by skorobogatova on 16 Sep 2023



Inserted: 23 apr 2023
Last Updated: 16 sep 2023

Year: 2023


We consider an area-minimizing integral current $T$ of codimension higher than $1$ in a smooth Riemannian manifold $\Sigma$. We prove that $T$ has a unique tangent cone, which is a superposition of planes, at $\mathcal{H}^{m-2}$-a.e. point in its support. In combination with works of the first and third authors, we conclude that the singular set of $T$ is countably $(m-2)$-rectifiable.