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Dirac equation written on the boundary of the Nutku helicoid space consistsof a system of ordinary differential equations. We tried to analyze this systemand we found that it has a higher singularity than those of the Heun'sequations which give the solutions of the Dirac equation in the bulk. We alsolose an independent integral of motion on the boundary. This facts explain whywe could not find the solution of the system on the boundary in terms of knownfunctions. We make the stability analysis of the helicoid and catenoid casesand end up with an appendix which gives a new example where one encounters aform of the Heun equation.

Singularity Structure and Stability Analysis of the Dirac Equation on the Boundary of the Nutku Helicoid Solution