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
Département de Mathématiques
Bâtiment 307
Faculté des Sciences d'Orsay Université Paris-Saclay F-91405 Orsay Cedex Tél. : +33 (0) 1-69-15-79-56 
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