2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140945There is an intrinsic notion of what it means for a contact manifold to be the smooth boundary of a Stein manifold. The same concept has another more extrinsic formulation, which is often used as a convenient working hypothesis. We give a simple proof that the two are equivalent. Moreover it is shown that, even though a border always exists, it's germ is not unique; nevertheless the germ of the Dolbeault cohomology of any border is unique. We also point out that any Stein fillable compact contact 3- manifold has a geometric realization in C^4 via an embedding, or in C^3 via an immersion.Complex VariablesDifferential GeometrySymplectic Geometry53D10; 32V15; 35N99text