Some questions in the value distribution theory of holomorphic mappings, and complex variations

In this paper we study the asymptotic properties of the order functions $T_q$, $q\in\overline{1,m}$, of holomorphic mappings $f\colon\mathbf C^m\to\mathbf C^n$ in terms of the complex variations of corresponding plurisubharmonic functions. We introduce a class of mappings for which we prove a quasisurjectivity theorem of Sokhotskii type and give the asymptotics of the order functions.
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