Proceedings of the American Mathematical Society

Author(s): Adrian Butscher
Journal: Proc. Amer. Math. Soc. 131 (2003), 1953-1964.
MSC (2000): Primary 58J05
Posted: October 24, 2002
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Abstract: Let

be a special Lagrangian submanifold of a compact Calabi-Yau manifold

with boundary lying on the symplectic, codimension 2 submanifold

. It is shown how deformations of

which keep the boundary of

confined to

can be described by an elliptic boundary value problem, and two results about minimal Lagrangian submanifolds with boundary are derived using this fact. The first is that the space of minimal Lagrangian submanifolds near

with boundary on

is found to be finite dimensional and is parametrized over the space of harmonic 1-forms of

satisfying Neumann boundary conditions. The second is that if

is a symplectic, codimension 2 submanifold sufficiently near

, then, under suitable conditions, there exists a minimal Lagrangian submanifold

near

with boundary on

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