45 research outputs found
Deformations of minimal Lagrangian submanifolds with boundary
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 parametrised 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 .Comment: Final version; to appear in Proceedings of the American Mathematical
Society. The presentation is somewhat cleaner in places and the result is
restated for a general Calabi-Yau settin