Student / postdoc PDE seminar: Multivalued harmonic functions

Seminar | February 2 | 4:10-5 p.m. | 740 Evans Hall

 Brian Krummel, UC Berkeley

 Department of Mathematics

Dirichlet energy minimizing multivalued functions were introduced by Almgren in his proof that the singular set of an n-dimensional area minimizing submanifold has Hausdorff dimension at most n-2. Such functions play a crucial role in the study of area minimizing submanifolds at branch point singularities, at which at least one tangent cone is a plane with integer multiplicity > 1. We will discuss how Dirichlet energy minimizing multivalued functions arose in Almgren's work. We will then cover the basic theory of Dirichlet energy minimizing multivalued functions, focusing on the study of singularities by means of frequency functions. As time allows, we will discuss my recent joint work with Neshan Wickraramsekera on the fine structure of singularities of Dirichlet energy minimizing multivalued functions.

 evans@math.berkeley.edu