ON LIMIT BRODY CURVES IN C<b><i><sup>n </sup></i></b>AND (C<b><sup>∗</sup></b>)<sup>2 </sup>

Abstract

In this paper, the conjecture on the Zalcmanness of Cn (n � 2) and (C�)2, which is posed in (8), is proved in the case where the derivatives of limit holomorphic curves are bounded. Moreover, several criteria for normality of families of holomorphic mappings are given.