Dirichlet polyhedra for cyclic groups in complex hyperbolic space

Phillips, Mark B.

doi:10.1090/S0002-9939-1992-1107276-1

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
DOI: https://doi.org/10.1090/S0002-9939-1992-1107276-1
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 -space centered at an arbitrary point 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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