A Symplectically Non-Squeezable Small Set and the Regular Coisotropic Capacity

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 proof involves a certain
Lagrangian submanifold of linear space, which was considered by M.
Audin and L. Polterovich. (Joint work with Jan Swoboda)