Quasi-Fuchsian, almost-Fuchsian, and nearly-Fuchsian manifolds

Speaker: Andrea Seppi (Università degli Studi di Torino)

Time: 2025-06-30 15:00
Zoom Meeting ID: 918 3593 2327 (Passcode: 544206)

Abstract:
In the first talk, I will give an overview of the study of quasi-Fuchsian manifolds via minimal surfaces, starting from the pioneering work of Uhlenbeck in the 1980s, that introduced the important class of almost-Fuchsian manifolds. I will talk about the relationship with holomorphic quadratic differentials, the problem of uniqueness of minimal surfaces, and mention some more recent developments. In the second talk, I will present a recent work with Nguyen and Schlenker, where we showed that every weakly almost-Fuchsian manifold (i.e. a containing a closed minimal surfaces with principal curvatures in [-1,1]) is actually nearly-Fuchsian (i.e. it contains a closed surface with principal curvatures in (-1,1)). I will provide the main elements of the proof and discuss some consequences.