The geometric structure of solutions to the two-valued minimal surface equation

Recently, Simon and Wickramasekera (J Differ Geom 75: 143-173, 2007) introduced a PDE method for producing examples of stable branched minimal immersions in R(3). This method produces two-valued functions u over the punctured unit disk in R(2) so that either u cannot be extended continuously across the origin, or G the two-valued graph of u is a C(1,alpha) a stable branched immersed minimal surface. The present work gives a more complete description of these two-valued graphs G in case a discontinuity does occur, and as a result, we produce more examples of C(1,alpha) stable branched immersed minimal surfaces, with a certain evenness symmetry.