2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156686We develop a method for preserving pseudoholomorphic curves in contact 3-manifolds under surgery along transverse links. This makes use of a geometrically natural boundary value problem for holomorphic curves in a 3-manifold with stable Hamiltonian structure, where the boundary conditions are defined by 1-parameter families of totally real surfaces. The technique is applied here to construct a finite energy foliation for every closed overtwisted contact 3-manifold.76 pages, 15 figures; typos correctedSymplectic GeometryAnalysis of PDEsDifferential Geometry32Q65; 57R17text