Symplectic capacity

Summary

A symplectic capacity is a number attached to symplectic manifolds, or to subsets of $\R^{2n}$, that measures their size. It is compatible with symplectic embeddings. It cannot grow under symplectic embeddings and is normalized so that a ball and a cylinder of the same radius have the same capacity. The existence of capacities is equivalent in strength to Gromov's non-squeezing theorem, and capacities are a main tool of quantitative symplectic topology.