3 problems

Let $\varepsilon_*$ be the maximal small-angle threshold for which $\mathbf{C}_{7,1,\theta}$ is strictly minimizing, and let $\varepsilon^*$ be the near-$\frac{\pi}{2}$ threshold f…

Let $M\subset(X^{n+1},\partial X,g,\sigma)$ be a minimizer of the capillary energy, and let $\operatorname{sing}(M)$ denote its singular set. Critical dimension conjecture. The bou…

Let $n$ and $k$ be in the ranges considered in the theorem establishing minimization for small contact angles, excluding $(n,k)\in\{(7,1),(7,5)\}$. Let…