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Abstract

Suppose M₁ and M₂ are two special Lagrangian submanifolds of Rtn with boundary that intersect transversally at one point p. The set M₁ cup M₂ is a singular special Lagrangian variety with an isolated singularity at the point of intersection. Suppose further that the tangent planes at the intersection satisfy an angle condition (which always holds in dimension n=3). Then, M₁ cup M₂ is regularizable; in other words, there exists a family of smooth, minimal Lagrangian submanifolds M_(alpha) with boundary that converges to M₁cup M₂ in a suitable topology. This result is obtained by first gluing a smooth neck into a neighbourhood of M₁ cap M₂ and then by perturbing this approximate solution until it becomes minimal and Lagrangian