Ros's conjecture on properly embedded minimal surfaces in hyperbolic 3-space

An open surface is a non-compact surface without boundary. Let $S$ be an open, connected, orientable surface. Ros's conjecture. Every such surface can be properly and minimally embedded in hyperbolic $3$-space $\mathbb{H}^3$. This conjecture asks whether every orientable topological surface of infinite type can occur as a properly embedded minimal surface in hyperbolic $3$-space; the source presents it as an open question following existence results for finite topological type.