8 problems

Even-modulus regularity conjecture. The conclusions of Theorem hold for $p$ even as well; that is, when $p$ is even, $\operatorname{Sing}(T)$ is $(m-1)$-rectifiable and, for every…

Flat-point conjecture.

Tangent-cone uniqueness conjecture. There is a unique tangent cone to $T$ at $p$.

White's discreteness conjecture. The union of the boundary and interior singular sets is discrete.

Boundary-measure conjecture.

White's finite-topology conjecture. The topology of any area-minimizing $2$-dimensional integral current is finite if its boundary is a real analytic curve.

Dimension conjecture. The Hausdorff dimension of the set of genuine boundary singularities is at most $m-2$.

Let $T$ be an $n$-dimensional absolutely area-minimizing integer rectifiable current in an open subset of $\mathbb{R}^{n+1}$ containing the origin. Near the origin, suppose that…