  In this article we obtain uniform estimates on the absorption of Brownian
motion by porous interfaces surrounding a compact set. An important ingredient
is the construction of certain resonance sets, which are hard to avoid for
Brownian motion starting in the compact set. As an application of our results,
we substantially strengthen the results of arXiv:1412.3960, and obtain when $d
\ge 3$, large deviation upper bounds on the probability that simple random walk
in $Z^d$, or random interlacements in $Z^d$, when their vacant set is in a
strongly percolative regime, disconnect the discrete blow-up of a regular
compact set from the boundary of the discrete blow-up of a box containing the
compact set in its interior. Importantly, we make no convexity assumption on
the compact set. It is plausible, although open at the moment, that the upper
bounds that we derive in this work match in principal order the lower bounds of
Xinyi Li and the second author (see arXiv:1310.2177) in the case of random
interlacements, and of Xinyi Li (see arXiv:1412.3959) for the simple random
walk.
