On J-holomorphic variational vector fields and extremal discs

Abstract

We prove that every $J$-holomorphic variational vector field can be realized as derivation ${\frac{d}{dt}}_{|t=0}{f}_t$ 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.

9 pages, typos and Lemma 6 corrected