4 problems

In the totally irrational setting, consider a minimal lamination by area-minimizing hypersurfaces with gaps, and suppose the construction produces complete, non-compact minimal hyp…

Singular-set conjecture. Suppose that $d\geq 8$. Then every function of locally least gradient $u:M\to\mathbf{R}$ has a singular set $S_u$ of codimension $8$, such that on…

Let $S\subset\mathbb{R}^3$ be a closed set whose one-dimensional Hausdorff measure is zero, and let $\mathcal{L}$ be a minimal lamination of $\mathbb{R}^3-S$. Fundamental singulari…

Consider the exhaustion of hyperbolic $3$-space by hyperbolic geodesic balls centered at the origin, together with compact minimal disks whose boundaries lie on the boundaries of t…