Ideal tetrahedral decompositions of hyperbolic 3-manifolds
The author gives a partial (affirmative) answer to a well-known conjecture that every finite-volume noncompact hyperbolic 3-manifold admits a decomposition into ideal tetrahedra. This answer is based on the fact due to \textit{D. B. A. Epstein} and \textit{R. C. Penner} [J. Differ. Geom. 27, 67-80 (1988; Zbl 0611.53036)] that such manifolds always admit decompositions into convex ideal polyhedra. Actually, the author proves the conjecture for manifolds that can be decomposed into two ideal polyhedra. Previously in 1994, M. Wada proved this conjecture (unpublished) for manifolds obtained by glueing of sides of one ideal polyhedron.
scientific article; zbMATH DE number 902853