In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely...

geometric group theory, an acylindrically hyperbolic group is a group admitting a non-elementary 'acylindrical' isometric action on some geodesic hyperbolic metric...

relatively hyperbolic groups are the fundamental groups of complete noncompact hyperbolic manifolds of finite volume. A group G is relatively hyperbolic with...

or the hyperbolic plane. Fuchsian groups are, by definition, discrete subgroups of the isometry group of the hyperbolic plane. A Fuchsian group that preserves...

"Hyperbolic groups" that introduced the notion of a hyperbolic group (also known as word-hyperbolic or Gromov-hyperbolic or negatively curved group),...

classical hyperbolic geometry and of trees. Hyperbolicity is a large-scale property, and is very useful to the study of certain infinite groups called Gromov-hyperbolic...

In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...

In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal...

In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space H3. The latter, identifiable...

subdivided, e.g. into hyperbolic and other Coxeter groups. However, there are multiple non-equivalent definitions for hyperbolic Coxeter groups. We use the following...