Appears in collection : 2025 - T2 - WS2 - Low-dimensional phenomena: geometry and dynamics

Convex co-compact hyperbolic manifolds contain a smallest non-empty geodesically convex subset, called their convex core. The "pleating" of the boundary of this convex core is recorded by a measured lamination, called the bending lamination, and Thurston conjectured that convex co-compact hyperbolic 3-manifolds are uniquely determined by their bending lamination. We will describe a proof of this conjecture (joint with Bruno Dular) and then explain how the statement is part of a broader picture concerning convex domains in hyperbolic manifolds.