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 | References | Similar Articles | Additional Information
Abstract: We prove that the Dirichlet fundamental polyhedron for a cyclic group generated by a unipotent or hyperbolic element acting on complex hyperbolic
-space centered at an arbitrary point
is bounded by the two hypersurfaces equidistant from the pairs
and
respectively. The proof relies on a convexity property of the distance to an isometric flow containing
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1992-1107276-1
Keywords:
Discrete groups,
fundamental domain,
complex hyperbolic space
Article copyright:
© Copyright 1992
American Mathematical Society