6 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 $n$ 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…

Bernstein–Breiner's conjecture. The maximally symmetric marginally stable pieces of the catenoids in a slab achieve the least area among all smooth minimal surfaces spanning the sa…

Let $\mathbb{S}^5$ be the unit sphere and let $\Sigma_H\subset\mathbb{S}^5$ be the hexagonal Legendrian minimal torus. For a surface $\Sigma\subset\mathbb{S}^5$, write…

Let $C$ be a solid cylinder, and let the top and bottom disks of $C$ contain two skew diameters. Consider surfaces spanning these two diameters, with any other boundary components…

Let $u$ be the parameter defining the box $\operatorname{BP}_u$, let $W_u:=\operatorname{BP}_u\cap\\{(x,y,z):|x|\leqslant 1\\}$, and let $\partial W_u$ be its boundary. Let…