4/1/2005

Neshan Wickramasekera
MIT

Existence and regularity of stable branched minimal hypersurfaces

I will describe the following local regularity theorem and its consequences: If an immersed stable minimal hypersurface having a small singular set is weakly close to a multiplicity 2 hyperplane in a ball, then in the interior, it is a branched 2-valued $C^{1, \alpha}$graph. I will also present an existence theorem for branched stable minimal hypersurfaces. The latter result is joint work with Leon Simon.