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We prove a coisotropic intersection result and deduce the following: 1. Lowerbounds on the displacement energy of a subset of a symplectic manifold, inparticular a sharp stable energy-Gromov-width inequality. 2. A stablenon-squeezing result for neighborhoods of products of unit spheres. 3.Existence of a "badly squeezable" set in $\mathbb{R}^{2n}$ of Hausdorffdimension at most $d$, for every $n\geq2$ and $d\geq n$. 4. Existence of astably 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 areaof a regular coisotropic submanifold of dimension $d$.

Coisotropic Displacement and Small Subsets of a Symplectic Manifold