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Jennifer Slimowitz - Length minimizing geodesics in the group of Hamiltonian diffeomorphisms
| 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.
