[2111.01614] Foliage structure measured at infinity of a quasi-Fuchsian manifold near a Fuchsian locus

Download the PDF of the paper entitled “Measured foliations at infinity of quasi-Fuchsian manifests near the Fuchsian locus” by Diptaishik Choudhury.

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overview: Consider foliage of a quasi-Fuchsian manifold measured at infinity. This is a natural analogy at infinity to bending stacking measured at the boundary of a convex core. Then, for $t>0$, a set of rational measurement leaf surfaces $(\mathsf{f}_{+},\mathsf{f}_{-})$ satisfying the closed hyperboloid $S$ is given. $t\mathsf{f}_{+}$ and $t\mathsf{f}_{-}$ are uniquely {leaf surfaces measured at infinity} of a quasi-Fuchsian manifold homeomorphic to $S It can be realized. \times \mathbb{R}$ and close enough to the Fuchsian locus. Here, reasonable means that the corresponding measured lamination is maximum. This proof is inspired by Bonahon’s proof of \cite{bonahon05} and shows that a quasi-Fuchsian manifold close to a Fuchsian locus can be uniquely determined by the data filling the bending stack measured at the boundary of its convex core. I’m here. Finally, interpret the result with the {half-pipe} geometry.