2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136615We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit sets, but are not convex cocompact.v2. Accepted version. Minor revisions incorporating referee's comments. v1. 21 pagesGeometric TopologyGroup Theorytext