Abstract
We discuss a PDE method for producing examples of immersed minimal surfaces in the
unit cylinder in
as graphs of two-valued functions over the punctured unit disk. These two-valued
functions can either be extended continuously across the origin, in which case the
two-valued graph is a stable branched minimal immersion, or we can give
an asymptotic description of the graphs near the vertical axis. Various
analogies to the theory of the Minimal Surface Equation will be illustrated.