6 problems

Let $V$ be a stationary $m$-dimensional varifold in $U\subseteq\mathbb{R}^{m+n}$, let $h$ be harmonic on $V$, meaning that for every $\varphi\in C_c^1(U)$, … 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