Regularity of minimizing p-harmonic maps into spheres

par Kasia Mazowiecka

lundi 5 juin 2023, 11:00 → 12:00 Europe/Paris

Bâtiment Buffon, salle RH04A (Université Paris-Cité (campus Grands Moulins))

Regularity of minimizing p-harmonic maps – i.e., minimizers of the Dirichlet p-energy among maps between two given manifolds – is known to depend on the topology of the target manifold. In particular, the case of maps into spheres has been studied intensively, but still some of the most basic questions concerning maps from B³ into S³ remain open. Minimizing maps in this context were shown to be regular when p=2 or p≥3, and recently also when 2<p<2.13, leaving a peculiar gap in between. I will discuss known approaches to the problem and how to prove regularity for 2<p<2.36 and 2.97<p<3, thus shrinking the gap. This is joint work with Michał Miśkiewicz (University of Warsaw).