In this paper, we deal with the problem of uniqueness for meromorphic functions in the whole complex plane $\mathbf{C}$ under some shared-value/set conditions in an angular domain instead of the whole plane. Results are obtained extending some results by Lin, Mori and Tohge [W. C. Lin, S. Mori and K. Tohge, Uniqueness theorems in an angular domain, Tohoku Math. J., 58 (2006), 509–527].

In this paper, we discuss three discreteness criterions of $n$-dimensional subgroup $G$ of $PU(1,n;\mathbf{C})$. This generalize some discreteness criterions established by J. Gilman [3], S. Yang and A. Fang [9].