|JENNIFER SLIMOWITZ, Université du Québec à Montréal, Montréal, Québec H3C 3P8, Canada|
|Length minimizing geodesics in the group of Hamiltonian diffeomorphisms|
To any symplectic manifold , one can associate the group Hamc(M) of compactly supported Hamiltonian diffeomorphisms of M. Hofer has constructed a norm on this group which can be used to define the notion of a length minimizing path. A new class of examples of length minimizing paths in Hamc(M) for M of dimension 2 or 4will be presented. The proofs rely on a technique described by Lalonde and McDuff using a new estimate on the Hofer-Zenhder capacity of certain manifolds.