  We show that any compact symplectic manifold (W,\omega) with boundary embeds
as a domain into a closed symplectic manifold, provided that there exists a
contact plane \xi on dW which is weakly compatible with omega, i.e. the
restriction \omega |\xi does not vanish and the contact orientation of dW and
its orientation as the boundary of the symplectic manifold W coincide. This
result provides a useful tool for new applications by Ozsvath-Szabo of
Seiberg-Witten Floer homology theories in three-dimensional topology and has
helped complete the Kronheimer-Mrowka proof of Property P for knots.
