Minimal area surfaces and fibered hyperbolic 3-manifolds

By work of Uhlenbeck, the largest principal curvature of any least area fiber of a hyperbolic 3 3 -manifold fibering over the circle is bounded below by one. We give a short argument to show that, along certain families of fibered hyperbolic 3 3 -manifolds, there is a uniform lower bound for the maximum principal curvatures of a least area minimal surface which is greater than one.