Length minimizing paths in the Hamiltonian diffeomorphism group
Abstract
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 C1-topology. The construction utilizes a continuation argument and chain level result in the Floer theory of Lagrangian intersections.
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