## Symplectic Capacities in Manifolds

### Volume 39 / 1997

Banach Center Publications 39 (1997), 77-87
DOI: 10.4064/-39-1-77-87

#### Abstract

Symplectic capacities coinciding on convex sets in the standard symplectic vector space are extended to any subsets of symplectic manifolds. It is shown that, using embeddings of non-smooth convex sets and a product formula, calculations of some capacities become very simple. Moreover, it is proved that there exist such capacities which are distinct and that there are star-shaped domains diffeomorphic to the ball but not symplectomorphic to any convex set.