Intersections of totally real and holomorphic disks (Q1325629)

The authors prove the following Theorem. Let \(f : \overline \Delta \to \mathbb{C}^ 2\) be a smooth embedding of the closed unit disk, holomorphic on \(\Delta\), and let \(g : \overline \Delta \to \mathbb{C}^ 2\) be a smooth totally real embedding such that \(f (\partial \Delta) = g (\partial \Delta)\). Then the intersection \(f(\Delta) \cap g (\Delta)\) is non-empty.