  We prove that for $n\geq2$ there exists a compact subset $X$ of the closed
ball in $R^{2n}$ of radius $\sqrt{2}$, such that $X$ has Hausdorff dimension
$n$ and does not symplectically embed into the standard open symplectic
cylinder. The second main result is a lower bound on the $d$-th regular
coisotropic capacity, which is sharp up to a factor of 3. For an open subset of
a geometrically bounded, aspherical symplectic manifold, this capacity is a
lower bound on its displacement energy. The proofs of the results involve a
certain Lagrangian submanifold of linear space, which was considered by M.
Audin and L. Polterovich.
