Improved decay rate in a stability theorem for hyperbolic metrics

Abstract

Recently, Ursula Hamenst\"adt and the author proved a stability result for finite volume hyperbolic metrics in dimension three that does not assume any upper volume bounds, but that requires an exponentially fine control of the metric in the thin part of the manifold. We use a bootstrap argument to extend the result allowing for a weaker exponential control of the metric. This is achieved by formulating an abstract axiomatic framework.