  We prove a coisotropic intersection result and deduce the following: 1. Lower
bounds on the displacement energy of a subset of a symplectic manifold, in
particular a sharp stable energy-Gromov-width inequality. 2. A stable
non-squeezing result for neighborhoods of products of unit spheres. 3.
Existence of a "badly squeezable" set in $\mathbb{R}^{2n}$ of Hausdorff
dimension at most $d$, for every $n\geq2$ and $d\geq n$. 4. Existence of a
stably exotic symplectic form on $\mathbb{R}^{2n}$, for every $n\geq2$. 5.
Non-triviality of a new capacity, which is based on the minimal symplectic area
of a regular coisotropic submanifold of dimension $d$.
