Structure of branch sets of minimal submanifolds
speaker: Neshan Wickramasekera (University of Cambridge)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 In particular, our estimates combined with earlier (unpublished) work of the speaker imply rectifiability results for branch sets and uniqueness of blow-ups at generic branch points for (a) stable minimal hypersurfaces near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.
timetable:
Fri 11 Oct, 10:00 - 10:50, Aula Dini
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