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Discreteness criteria and algebraic convergence theorem for subgroups in \(\text{PU}(1,n;\mathbb C)\). (English) Zbl 1139.30324

Summary: We study the discreteness criterion for non-elementary subgroups in \(\text{PU}(1,n;\mathbb C)\). Several discreteness criteria are obtained. As an application, the convergence theorem of discrete subgroups in \(\text{PU}(1,n;\mathbb C)\) is discussed.

MSC:

30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
22E40 Discrete subgroups of Lie groups
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
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