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.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/4234
[3] http://www.mpim-bonn.mpg.de/de/node/3050