Orateur
Rémy Rodiac
Description
We will discuss the existence of critical points of the $n$-Ginzburg-Landau energy in the unit ball of $\mathbb R^n$ with prescribed degree one on the boundary. We will first prove that there does not exist any minimizer of this energy among maps with prescribed degree $d\neq 0$. Then we will show that we can devise a min-max scheme which allows us to prove the existence of critical points with prescribed degree one 1 if $\epsilon$, the inverse of the Ginzburg-Landau parameter, is large enough. A bubbling analysis is necessary because of the lack of compactness of the problem. This is a joint work with Dorian Martino and Katarzyna Mazowiecka.