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Dirichlet polyhedra for cyclic groups in complex hyperbolic space

Author: Mark B. Phillips
Journal: Proc. Amer. Math. Soc. 115 (1992), 221-228
MSC: Primary 32H20; Secondary 51M10, 51M20
MathSciNet review: 1107276
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Abstract: We prove that the Dirichlet fundamental polyhedron for a cyclic group generated by a unipotent or hyperbolic element $ \gamma $ acting on complex hyperbolic $ n$-space centered at an arbitrary point $ w$ is bounded by the two hypersurfaces equidistant from the pairs $ w,\gamma w$ and $ w,{\gamma ^{ - 1}}w$ respectively. The proof relies on a convexity property of the distance to an isometric flow containing $ \gamma $.

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Keywords: Discrete groups, fundamental domain, complex hyperbolic space
Article copyright: © Copyright 1992 American Mathematical Society