Mathematics – Differential Geometry
Scientific paper
2001-08-28
Mathematics
Differential Geometry
30 pages, 1 figure, Latex
Scientific paper
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.
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