23/07/17 13:31:41.79 GpeoaFRE.net
\begin{theorem}$\left(\hat{\Omega}, \displaystyle\left(\frac{du_1d\overline{u_1}}{({\rm Im }u_1)^2}+\frac{du_2d\overline{u_2}}{({\rm Im} u_2)^2} \right)|_{\hat{\Omega}}\right)$ is $L^2$-convex. \end{theorem}
Proof. Since the canonical bundle of $\hat{\Omega}$ is trivial as $A$ leaves $du_1\wedge du_2$ invariant, it is easy to see from [Dm] or [Oh-1] that Theorem 1 implies the solvability of the $\dbar$-equation with $L^2$ estimates which yields the assertion. \qed\\