Screw Motion Invariant Minimal Surfaces from Gluing Helicoids

Abstract

We consider families of embedded, screw motion invariant minimal surfaces in ${\mathbb{R}}^3$ which limit to parking garage structures. We derive balance equations for the nodal limit and regenerate to obtain surfaces corresponding to solutions. We thus prove the existence of many new examples with helicoidal or planar ends.

28 pages, 20 figures