Measured foliations at infinity of quasi-Fuchsian manifolds

Abstract

Let $(\lambda^+(M),\lambda^-(M))$ denote the pair of measured foliations at the boundary at infinity $\partial_\infty$ of a quasi-Fuchsian manifold $M$. We prove that $(\lambda^+(M),\lambda^-(M))$ is filling if $M$ is close to being Fuchsian. We also show that given any filling pair $(\alpha_1,\alpha_2)$ of measured foliations, and every small enough $t>0$, the pair $(t\alpha_1,t\alpha_2)$ is realised as the pair of measured foliations at infinity of some quasi-Fuchsian manifold $M$. This answers questions of Schlenker near the Fuchsian locus.