Screw Motion Invariant Minimal Surfaces from Gluing Helicoids

TL;DR

This paper constructs new screw motion invariant minimal surfaces in three-dimensional space by analyzing their limits to parking garage structures and solving associated balance equations, expanding the known family of such surfaces.

Contribution

It introduces a method to generate many new embedded minimal surfaces with helicoidal or planar ends using gluing techniques and balance equations.

Findings

Existence of numerous new embedded minimal surfaces with screw symmetry.

Surfaces limit to parking garage structures, linking topology and geometry.

Method applicable to constructing surfaces with specified asymptotic behavior.

Abstract

We consider families of embedded, screw motion invariant minimal surfaces in $\R^3$ 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.