Acylindrical surfaces in 3-manifolds (Q1907021)

A closed, incompressible surface in a 3-manifold is called acyclic if its complement has no incompressible and boundary-incompressible annulus. Using properties of minimal surfaces in hyperbolic manifolds the author shows that the genus of an acylindrical surface is bounded from above by a function which depends on the volume of the underlying manifold alone. As a corollary one obtains the result that the set of all acylindrical surfaces in a compact, orientable 3-manifold is finite (mod isotopy).