On the Asymptotics of Convex Core Volumes of Once-Punctured Torus Groups

Abstract

We study the asymptotic behavior of the convex core volume for a sequence of quasi-Fuchsian manifolds $Q({\psi }^{-n}X,{\psi }^{n}X)$ associated with a pseudo-Anosov mapping class $\psi$ on a once-punctured torus. We prove that the volume of the convex core differs from $2n$ times the volume of the mapping torus of $\psi$ by at most a uniformly bounded constant.

31 pages, 4 figures