Essential surfaces in hyperbolic three-manifolds
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This dissertation is concerned with existence and behavior problems for essential surfaces in hyperbolic three-manifolds. In Chapter 2, we provide new examples of finite volume hyperbolic manifolds which are not fibered, but are virtually fibered. In Chapter 3, we prove that there are Dehn fillings arbitrarily close to infinity in the hyperbolic Dehn surgery space of the figure eight knot complement in which some closed totally geodesic surface compresses.