Classification in the solid torus

Classify all minimal Möbius bands and annuli in \(\mathbb{D}^2\times\mathbb{S}^1\).

Background

The paper notes that quotients of suitable dilations of the Euclidean helicoid provide examples of minimal Möbius bands and annuli in the solid torus. A complete classification of such examples is left as a separate problem in rotationally symmetric geometry.