Length minimizing paths in the Hamiltonian diffeomorphism group

On any closed symplectic manifold, we construct a path-connected neighborhood of the identity in the Hamiltonian diﬀeomorphism group with the property that each Hamiltonian diﬀeomorphism in this neighborhood admits a Hofer and spectral length minimizing path to the identity. This neighborhood is open in the $C^1$-topology. The construction utilizes a continuation argument and chain level result in the Floer theory of Lagrangian intersections.

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Published 1 January 2008