On limit Brody curves in ${\mathbb{C}}^n$ and $({\mathbb{C}}^{\ast }{)}^2$

Abstract

In this paper, the conjecture on the Zalcmanness of ${\mathbb{C}}^n(n\ge 2)$ and $({\mathbb{C}}^{\ast }{)}^2$, which is posed in \cite{Do}, 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.

13 pages