Injectivity radii of hyperbolic polyhedra

Details Injectivity radii of hyperbolic polyhedra Injectivity radii of hyperbolic polyhedra

1998-12-11

arxiv.org/abs/math/9812067v3

Pacific J. Math. 197 (2001), no. 2, 369--382

Mathematics

Geometric Topology

14 pages, 9 figures. Replaced with published version

Scientific paper

We define the injectivity radius of a Coxeter polyhedron in H^3 to be half
the shortest translation length among hyperbolic/loxodromic elements in the
orientation-preserving reflection group. We show that, for finite-volume
polyhedra, this number is always less than 2.6339..., and for compact polyhedra
it is always less than 2.1225... .

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