On the singular set of minimizing harmonic maps (IN PERSON TALK IN 383N)

Minimizing harmonic maps (i.e., minimizers of the Dirichlet integral) with prescribed boundary conditions are known to be smooth outside a singular set of codimension 3. I will present an extension of Almgren and Lieb’s linear law on the bound of the singular set. Next, I will investigate how the singular set is affected  by small perturbations of the prescribed boundary map and present a stability theorem, which is an extension of Hart and Lin’s result. I will also discuss possible target manifolds and the optimality of our assumptions. This is joint work with Michał Miśkiewicz and Armin Schikorra.