On s-Stability of W^{s,n/s}-minimizing maps between spheres in homotopy classes

par Katarzyna Mazowiecka (Institute of Mathematics, University of Warsaw)

mardi 7 oct. 2025, 11:00 → 12:30 Europe/Paris

Salle de réunion Fizeau (LJAD)

We consider maps between spheres Sⁿ to S^ℓ that minimize the Sobolev−space energy W^s,n/s for some s ∈ (0,1) in a given homotopy class. The basic question is∶ in which homotopy class does a minimizer exist? This is a nontrivial question since the energy under consideration is conformally invariant and bubbles can form. Sacks−Uhlenbeck theory tells us that minimizers exist in a set of homotopy classes that generates the whole homotopy group 𝜋_n(𝑆^ℓ). Explicit examples are known if n/s = 2 or s=1.  

In this talk we are interested in the stability of the above question in dependence of s. We can show that as s varies locally, the set of homotopy classes in which minimizers exist can be chosen stable. We also discuss that the minimum W^s,n/s-energy in homotopy classes is continuously depending on s.  

Joint work with A. Schikorra (University of Pittsburgh)