Symplectic embeddings into cylinders for certain symplectic manifolds

We present a proof of a result on displaceability of subsets of symplectic manifolds satisfying certain conditions one of which is that the subset is precompact in a connected neighborhood that symplectically embeds into $\mathbb{R}^{2n}$. The proof utilizes an inequality between the displacement energy and the cylindrical capacity for subsets of $\mathbb{R}^{2n}$ to obtain an inequality for subsets of the symplectic manifold. We also state a corollary which utilizes other results on nondisplaceable Lagrangians.