On J-holomorphic variational vector fields and extremal discs

We prove that every $J$-holomorphic variational vector field can be realized as derivation ${\frac{d}{dt}}_{\mathrm{\mid }t=0}{f}_t$ where $(f_t)$ is a one parametric family of $J$-holomorphic discs. Furthermore, we discuss properness of an extremal $J$-holomorphic disc in a bounded pseudoconvex domain.