3 problems

McMullen's conjecture. The convex core $C(N)$ does not contain an embedded ball of radius $L$, where $L$ depends on the number of generators of $\pi_1(N)$.

Let $M$ be a geometrically finite hyperbolic 3-manifold, meaning that its convex core has finite volume. Its convex core is the intersection of all closed totally convex subsets of…

Mess's conjecture. There is a unique maximal globally hyperbolic $\mathbb{A}\mathbbm{d}\mathbb{S}^3$ manifold $N$ such that the induced metric on the boundary of the convex core of…