Moduli of special Lagrangians with boundary, I: Unobstructed Deformations

This article studies the deformation problem for compact special Lagrangians with boundary in a Calabi--Yau manifold, with each boundary component constrained along a given Lagrangian submanifold. The tangent vectors generating such deformations are identified with harmonic 1-forms vanishing on the boundary of the special Lagrangian, and the deformation generated by any such tangent vector is unobstructed. Consequently, the moduli space of special Lagrangians with boundary is a smooth manifold whose dimension equals the dimension of the first relative cohomology of the special Lagrangian.