4 problems

Let $M$ be a connected surface of finite topology, with genus $g$ and $r>2$ ends. Finite topology conjecture. The surface $M$ can be properly minimally embedded in $\mathbb{R}^3$ i…

Let $n\geq4$, let $G=\operatorname{O}(n)\times\operatorname{O}(n)$, and consider $G$-equivariant minimal embeddings of the sphere $S^{2n-1}$ into the round sphere $\mathbb{S}^{2n}$…

Let $T^3=S^1\times S^1\times S^1$ be the three-dimensional torus, embedded minimally in the round four-dimensional sphere $\mathbb{S}^4$. Two embeddings are considered equivalent i…

Let $\Omega\subset\mathbb{R}^3$ be the particular bounded domain, smooth except at one point, described by Ferrer, Martín, Meeks and Nadirashvili. An open surface with compact, pos…