  On a geometric model for complex networks (introduced by Krioukov et al.) we
investigate the bootstrap percolation process. This model consists of random
geometric graphs on the hyperbolic plane having $N$ vertices, a dependent
version of the Chung-Lu model. The process starts with infection rate $p=p(N)$.
Each uninfected vertex with at least $\mathbf{r}\geq 1$ infected neighbors
becomes infected, remaining so forever. We identify a function $p_c(N)=o(1)$
such that a.a.s.\ when $p\gg p_c(N)$ the infection spreads to a positive
fraction of vertices, whereas when $p\ll p_c(N)$ the process cannot evolve.
Moreover, this behavior is "robust" under random deletions of edges.
