The local maxima of maximal injectivity radius among hyperbolic surfaces

Abstract

The function on the Teichmueller space of complete, orientable, finite-area hyperbolic surfaces of a fixed topological type that assigns to a hyperbolic surface its maximal injectivity radius has no local maxima that are not global maxima.Comment: Dramatically shortened (now 12 pp.), and introductory material simplified, following a referee's suggestion