2010/06/09 by Antoine Gournay, Gournay, Antoine
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #math.DG
paper · pdf · doi:10.48550/arxiv.1006.1775
24 pages
arxiv created 2010/06/09 · openalex publication_date 2010/06/09 · arxiv updated 2010/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gromov has shown how to construct holomorphic maps of the plane to a complex manifold with prescribed values on a lattice. In the present paper, a similar interpolation theorem for pseudo-holomorphic maps from the cylinder S to an almost-complex manifold (M,J) is proved. Properties of the space of pseudo-holomorphic maps from S to (M,J) are derived, in particular a lower bound for the size of this space (in terms of mean dimension). When M is a moduli space of curves, this gives a construction of non-compact complex surfaces. The methods involve an infinite number of surgeries. On the way, a refinement of the gluing process for two pseudo-holomorphic curves is obtained, establishing the geometric behavior of two glued pseudo-holomorphic curves.