2001/08/28 by Sema Salur, Salur, Sema
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.math/0108182
30 pages, 1 figure, Latex
arxiv created 2001/08/28 · openalex publication_date 2001/08/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to prove a gluing theorem for a given special Lagrangian submanifold of a Calabi-Yau 3-fold. The proof will be an adaption of the gluing techniques in J-holomorphic curve theory. It is a well known procedure in geometric analysis to construct new solutions to a given nonlinear partial differential equation by gluing known solutions. First an approximate solution is constructed and then using analytic methods it is perturbed to a real solution. In this paper the gluing theorem will be used for smoothing a singularity of a special Lagrangian submanifold. In particular, we will show that given a special Lagrangian submanifold L of a Calabi-Yau manifold X with a particular codimension-two self intersection K it can be approximated by a sequence of smooth special Lagrangian submanifolds and therefore L is a limit point in the moduli space.