Let $(M,J,\omega)$ be a symplectic manifold with a compatible almost complex structure, $D$ be the closed unit disk in $\mathbb{C}$, and $u:(D,i)\to (M,J)$ be a $(J,i)$-holomorphic map.

*Question*: Assume $u|_{\partial D}$ is constant, does this imply $u$ is a constant map?