  Let $d\geq 2$. We consider an i.i.d. supercritical bond percolation on
$\mathbb{Z}^d$, every edge is open with a probability $p>p_c(d)$, where
$p_c(d)$ denotes the critical point. We condition on the event that $0$ belongs
to the infinite cluster $\mathcal{C}_\infty$ and we consider connected
subgraphs of $\mathcal{C}_\infty$ having at most $n^d$ vertices and containing
$0$. Among these subgraphs, we are interested in the ones that minimize the
open edge boundary size to volume ratio. These minimizers properly rescaled
converge towards a translate of a deterministic shape and their open edge
boundary size to volume ratio properly rescaled converges towards a
deterministic constant.
