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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 $(M, \omega)$, 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.



 

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