Wednesday, February 23, 2022 3:15 PM
Katarzyna Mazowiecka (University of Warsaw)

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.