Existence of a somewhere injective pseudo-holomorphic disc

Abstract.

Given a smooth totally real submanifold ${\cal L}$ in an almost complex manifold (M,J) and a J-holomorphic disc with boundary in ${\cal L}$, by restriction of the initial disc and factorization, one gets a smooth simple J-holomorphic curve still with boundary in ${\cal L}$. As a consequence one gets a proof of the Arnold-Givental conjecture for a class of Lagrangian submanifolds in a symplectic manifold.