Capacity of a multiply-connected domain and nonexistence of Ginzburg-Landau minimizers with prescribed degrees on the boundary

Leonid Berlyand, Dmitry Golovaty, Volodymyr Rybalko

Suppose that $\omega \subset \Omega \subset R^2$. In the annular domain $A=\Omega \setminus \bar{\omega }$ we consider the class $J$ of complex valued maps having degree 1 on $\partial \Omega$ and on $\partial \omega$.…