Dynamics of self-joinings of hyperbolic manifolds

This is a classical result of Sullivan that for a convex cocompact hyperbolic manifold M the critical exponent of π1(M) is the same as the Hausdorff dimension of its limit set. We study analogous phenomena in a higher-rank setting. This is my first work at Yale, joint with Prof. Yair N. Minsky and Prof. Hee Oh.