4 problems

Multiplicity conjecture. There exist multiple translation-invariant genus 2 helicoids and multiple genus 2 helicoids.

Uniqueness conjecture. These surfaces are the unique minimal surfaces with these properties.

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…

Hoffman–Weber–Wolf conjecture. The surface $\mathcal{H}$ is the same surface as the one produced by Hoffman, Karcher, and Wei, and is the unique symmetric genus-one helicoid in…