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Discreteness criteria based on a test map in \(\mathrm{PU}(n, 1)\). (English) Zbl 1270.30012

Summary: The discreteness of isometry groups in complex hyperbolic space is a fundamental problem. In this paper, discreteness criteria of a \(n\)-dimensional subgroup \(G\) of \(\mathrm{SU}(n, 1)\) are investigated by using a test map which may not be in \(G\).

MSC:

30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
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