  Motivated by classical theorems on minimal surface theory in compact
hyperbolic three-manifolds, we investigate the questions of existence and
deformations for least area minimal surfaces in complete noncompact hyperbolic
three-manifold of finite volume. We prove any closed immersed incompressible
surface can be deformed to a closed immersed least area surface within its
homotopy class in any cusped hyperbolic three-manifold. Our techniques
highlight how special structures of these cusped hyperbolic three-manifolds
prevent any least area minimal surface going too deep into the cusped region.
