  Denote by $E_\epsilon$ the Ginzburg-Landau functional in the plane and let
$\tilde u_\varepsilon$ be the radial solution to the Euler equation associated
to the problem $\min \left\{E_\varepsilon(u,B_1): \>\left. u\right\vert
_{\partial B_{1}}=(\cos \vartheta,\sin \vartheta)\right\}$. Let $\Omega\subset
\R^2$ be a smooth, bounded domain with the same area as $B_1$. Denoted by
$$\mathcal{K}=\left\{v=(v_1,v_2) \in H^1(\Omega;\R^2):\> \int_\Omega
v_1\,dx=\int_\Omega v_2\,dx=0,\> \int_\Omega |v|^2\,dx\ge \int_{B_1} |\tilde
u_\varepsilon|^2\,dx\right\},$$
  we prove $$ \min_{v \in \mathcal{K}} E_\varepsilon (v,\Omega)\le
E_\varepsilon (\tilde u_\varepsilon,B_1). $$
