Deformations of non-compact complex curves and envelopes of meromorphy of spheres

The paper discusses the properties of the envelopes of meromorphy of neighbourhoods of symplectically immersed two-spheres in complex Kahler surfaces. The method used to study the envelopes of meromorphy is based on Gromov's theory of pseudoholomorphic curves. The exposition includes a construction of a complete family of holomorphic deformations of a non-compact complex curve in a complex manifold parametrized by a finite-codimensional analytic subset of a Banach ball. The existence of this family is used to prove a generalization of Levi's continuity principle, which is applied to describe envelopes of meromorphy.