On the boundary of convex hyperbolic manifolds
Organizers
Speaker
Time
Tuesday, October 21, 2025 3:00 PM - 4:00 PM
Venue
A7-201
Online
Zoom 388 528 9728
(BIMSA)
Abstract
The study of convex co-compact hyperbolic manifolds from the data on their convex subdomains has long been a topic of study. Bers’ double uniformization theorem establishes a complete correspondence between the deformation space of such manifolds and the conformal structure on their ideal boundary. Thurston showed that any convex co-compact hyperbolic manifold contains a smallest compact convex domain with the same homotopy type, called the convex core. He also conjectured that there is a one-to-one correspondence between the invariants of the convex core boundary and the deformation space of the 3-dimensional manifold. Later, the work of Labourie and Schlenker established a one-to-one correspondence between the induced metric on the boundary of smoothly embedded convex subdomains and the deformation space of the 3-dimensional manifold. This talk will focus on the relation between convex co-compact hyperbolic 3-manifolds and the invariants induced on the boundary of their convex subdomains, with focusing on what happens when these invariants are combined. We will also introduce globally hyperbolic AdS manifolds and discuss how convex domains in AdS interact with their boundary data and the universal Teichmüller space.