Date: March 3, 2026, 1-2 PM EST

Speaker: Armin Schikorra (University of Pittsburgh)

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

Abstract:

We consider maps between spheres S^n to S^ell that minimize the
Sobolev-space energy W^{s,n/s} for some s in (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
pi_{n}(S^ell). In some situations explicit examples are known if
n/s = 2 or s=1.

In our 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.

Location: 1146 Faculty/Administration Building (Nelson Library)

Link: Link: https://wayne-edu.zoom.us/j/98693739093?pwd=wrzcgvyxMFfqar3ognCZjIpk4UsSfi.1