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Geodesic flow on ideal polyhedra. (English) Zbl 0904.52004
The authors define an \(n\)-dimensional ideal polyhedron to be a complete, locally finite union of ideal \(n\)-dimensional hyperbolic polytopes, glued along \((n-1)\)-faces, with at least two polytopes meeting in each \((n-1)\)-face. In their main result, the authors assert the density of closed geodesics and the existence of dense geodesics for finite ideal polyhedra.
Reviewer: W.Ballmann (Bonn)

MSC:
52B11 \(n\)-dimensional polytopes
53C20 Global Riemannian geometry, including pinching
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
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