4/15/2005

Michael Wolf
Rice University

Minimal Desingularizations of Planes in Space

We prove that there is only one way to 'desingularize' the intersection of two planes in space to and obtain a periodic minimal surface as a result. The proof is mostly an exercise in Teichmuller theory: we translate the geometry of minimal surface in space into a statement about a moduli space of flat structures on Riemann surfaces, and thenstudy deformation theory and degenerations in this moduli space to prove the result.