Structure of branch sets of minimal submanifolds

Neshan Wickramasekera

(University of Cambridge)

Date: Oct 11, 2013, time: 10:00

Abstract. The talk will be based on results from an on-going project
(joint with Brian Krummel) aimed at understanding the local structure
of sets of branch point singularities of various classes of minimal
varieties and multi-valued harmonic functions. For these classes, the work
thus far establishes a set of new a priori estimates, valid near
multiplicity 2 branch points, that are analogous to those
established in L. Simon's pioneering work in the early 90's on the
structure of singularities of minimal submanifolds in compact, multiplicity 1
classes satisfying a certain integrability hypothesis.
In particular, our estimates
combined with earlier (unpublished) work of the speaker imply
rectifiability results for
branch sets and uniqueness of blow-ups at generic branch points for
(a) stable minimal hypersurfaces near density 2 branch points and (b)
two-valued energy minimizing and $C^{1,\alpha}$ harmonic
functions.