Measured foliations at boundary at infinity of quasi-Fuchsian manifolds close to the Fuchsian locus

YMSC Topology Seminar

Organizers：

陈伟彦、高鸿灏、黄意、林剑锋

Speaker：

Diptaishik CHOUDHURY (YMSC)

Time：

Thur., 16:00-17:00, Sept. 19, 2024

Venue：

B725, Shuangqing Complex Building A

清华大学双清综合楼A座B725

Online：

Zoom meeting ID: 405 416 0815

Passcode: 111111

Title：

Measured foliations at boundary at infinity of quasi-Fuchsian manifolds close to the Fuchsian locus

Abstract:

We consider the horizontal measured foliations induced by the Schwarzian derivatives associated to each component of the boundary at infinity of a quasi-Fuchsian manifold. We then can ask if under certain conditions these can uniquely parametrise the manifold. We will show a proof of the fact that given a pair of measured foliations which fill, have only 3-pronged singularities and with their measure scaled suitably small enough, can be realised as the measured foliations at infinity of a quasi-Fuchsian manifold which is sufficiently close to the Fuchsian locus. The proof is inspired by that of Bonahon which shows that a quasi-Fuchsian manifold close to the Fuchsian locus can be uniquely parametrised by the pair of filling bending lamination on the boundary of the convex core.