  In this note we establish the existence of a new type of rigidity of
symplectic embeddings coming from obligatory intersections with symplectic
planes. More precisely, we prove that if a Euclidean ball is symplectically
embedded in the Euclidean unit ball, then it must intersect a sufficiently fine
grid of two-codimensional pairwise disjoint symplectic planes. Inspired by
analogous terminology for Lagrangian submanifolds, we refer to these
obstructions as symplectic barriers.
