Filling real hypersurfaces by pseudoholomorphic discs (Q941864)

Since the fundamental work of \textit{M. Gromov} [Invent. Math. 82, 307--347 (1985; Zbl 0592.53025)], pseudoholomorphic curves have become an object of intensive research because of their remarkable applications in symplectic geometry and low dimensional topology. Pseudoholomorphic discs with boundaries in a prescribed real manifold play an important role, and are called Bishop discs. The main result of the present work is the following: Theorem. Let \(E\) be a smooth real hypersurface in an almost complex manifold \((M, J)\). Assume that the set of all points where the Levi form of \(E\) vanishes identically has empty interior. Also assume that \(E\) contains no \(J\)-complex hypersurface passing through a point \(p\in E\). Then the Bishop discs of \(E\) fill a one-sided neighborhood of \(p\).