- 04 Mag 2022
Measured foliations at infinity of quasi-fuchsian manifolds near the Fuchsian locus
Quasi-Fuchsian manifolds, topologically, are hyperbolic 3 manifolds M that are homeomorphic to SxR, where S is a closed surface with genus g >1 . The “boundary at infinity of M” consists of two copies of S and we focus on the horizontal measured foliation of the Schwarzian derivatives obtained by uniformizing the two respective complex structures. We call them the “measured foliations at infinity of a quasi-Fuchsian manifold”. Independently, measured foliations on S are well-studied objects. We discuss how given a pair of measured foliations (F,G) that fill a closed hyperbolic surface, tF and tG (where t>0 is small enough) can be realized as the measured foliations at infinity of a quasi-Fuchsian manifold which is sufficiently close to being Fuchsian. Starting from the definitions, the plan of the talk will be to give an idea of the setting of the theorem and see how it draws parallels to the case of bending measured laminations on the boundary of the convex core.