非线性泛函分析讨论班：On s-Stability of W^{s,n/s}-minimizing maps between spheres in homotopy classes

中科院数学与系统科学研究院

数学研究所

学术报告

非线性泛函分析讨论班

报告人：Armin Schikorra (University of Pittsburgh)

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

时  间：2024.07.12（星期五）10:30-11:30 

地  点：S813

摘  要：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.