  In this paper, we study the Ginzburg-Landau equations for a two dimensional
domain which has small size. We prove that if the domain is small, then the
solution has no zero, that is no vortex. More precisely, we show that the order
parameter $\Psi$ is almost constant. Additionnally, we obtain that if the
domain is a disc of small radius, then any non normal solution is symmetric and
unique. Then, in the case of a slab, that is a one dimensional domain, we use
the same method to derive that solutions are symmetric. The proofs use a priori
estimates and the Poincar\'e inequality.
