On the size of the singular set of minimizing harmonic maps

Jeudi 4 février 14:00-15:00 - Katarzyna Mazowiecka - Université Catholique de Louvain (UCL)

Résumé : 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 consider mappings from an n-dimensional domain with values in the two dimensional sphere. 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 extensions to different target manifolds and the optimality of our assumptions. This is joint work with Michał Miśkiewicz and Armin Schikorra.

Lieu : visioconférence

On the size of the singular set of minimizing harmonic maps  Version PDF