We study a d-dimensional branching Brownian motion, among obstacles scattered

according to a Poisson random measure with a radially decaying intensity. Obstacles

are balls with constant radius and each one works as a trap for the whole motion when

hit by a particle. Considering a general offspring distribution, we derive the decay

rate of the annealed probability that none of the particles hits a trap,

asymptotically, in time. 

This proves to be a rich problem, motivating the proof of a general result about the speed 

of branching Brownian motion conditioned on

non-extinction. We provide an appropriate `skeleton-decomposition' for the underlying

Galton-Watson process when supercritical, and show that the `doomed particles' do 

not contribute to the asymptotic decay rate.

This is joint work with Mine Caglar and Mehmet Oz.