Packing problems have long been a topic of interest. Traditionally, efforts had been focused on Euclidean space, but as interest in hyperbolic space has grown, many of the Euclidean problems have been translated into the hyperbolic arena, in which the problems are almost always vastly more complicated. The particular packing problem of interest here is a hyperbolic version of packing congruent ...

We say that a group G is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. We prove that the class of acylindrically hyperbolic groups coincides with many other classes studied in the literature, e.g., the class Cgeom introduced by Hamenstädt, the class of groups admitting a non-elementary weakly properly discontinuous action on a hyperbolic spac...

A generalized hyperbolic tetrahedra is a polyhedron (possibly noncompact) with finite volume in hyperbolic space, obtained from a tetrahedron by the polar truncation at the vertices lying outside the space. In this paper it is proved that a volume formula for ordinary hyperbolic tetrahedra devised by J. Murakami and M. Yano can be applied to such ones. There are two key tools for the proof; one...