6 problems

Let $V$ be a stationary integer rectifiable varifold, let $x_0$ be a point with a unique flat tangent cone, let $\Theta(V,x_0)$ denote its density at $x_0$, and let…

Let $V$ be a stationary varifold, let $x_0\in{\rm spt}(V)\cap U$, and let $\mathcal{M}$ be a classical smooth minimal $m$-dimensional surface such that … The unique-continuation co…

Let $V$ and $x_0$ satisfy the assumptions of the flat tangent-cone regularity conjecture. The high-order contact conjecture. There is a smooth classical minimal $m$-dimensional gra…

Let $V$ be a stationary integer rectifiable $m$-dimensional varifold, and let its interior singular set be the nonregular points in the interior. The measure-zero conjecture. The i…

Let $V$ be a stationary integer rectifiable $m$-dimensional varifold, and let its interior singular set consist of the points of ${\rm spt}(V)$ that are not regular. The codimensio…

Smooth approximation conjecture. There is a smooth classical minimal $m$-dimensional graph $\mathcal{M}$ in some neighborhood of $x_0$ such that