Free group Cayley graph and measure decompositions

I will talk about convex-cocompact representations of finitely generated free group $F_g$ into $\mathrm{PSL}(2,\mathbb C)$. First I will talk about Schottky criterion. There are many ways of characterizes Schottky group. In particular, convex hull entropy criterion, Hausdorff dimension criterion. In addition we can also construct measure decomposition on Cayley graph, which is a generalization of the Culler-Shalen decomposition, gives criterion on primitive sets. And, I will discuss primitive curves in hyperbolic Handlebody that are Schottky. This is joint work with Jim Anderson.