Physical Sciences and Mathematics Commons^™

The Spinor Representation Of Minimal Surfaces, Rob Kusner, Nick Schmitt

Mathematics and Statistics Department Faculty Publication Series

The spinor representation is developed and used to investigate minimal surfaces in R^3 with embedded planar ends. The moduli spaces of planar-ended minimal spheres and real projective planes are determined, and new families of minimal tori and Klein bottles are given. These surfaces compactify in S^3 to yield surfaces critical for the M¨obius invariant squared mean curvature functional W. On the other hand, all Wcritical spheres and real projective planes arise this way. Thus we determine at the same time the moduli spaces of W-critical spheres and real projective planes via the spinor representation.