Minimal area surfaces and fibered hyperbolic $3$-manifolds

Abstract

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

arXiv comment14 pages. Comments are welcome! v2: minor changes incorporating comments of the referee; final version to appear in PAMS