On the Area of Minimal Surfaces in a Slab

Abstract

Abstract. Consider a non-planar orientable minimal surface Σ in a slab which is possibly with genus or with more than two boundary components. We show that there exists a catenoidal waist W in the slab whose flux has the same vertical component as Σ such that Area(Σ) ≥ Area(W), provided the intersections of Σ with horizontal planes have the same orientation.

Symmetry and Rigidity of Minimal Surfaces with Plateau-like Singularities

“…Namely in [BB14] the authors show that an appropriate piece of the catenoid has the least area among minimal annuli whose boundaries lie in two fixed parallel planes. was generalized in [CD16] who increased the class of competitors to a larger class of (smooth) minimal surfaces of different topological type. One may ask the same question in the class of singular minimal Plateau surfaces.…”