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Length minimizing paths in the Hamiltonian diffeomorphism group

Peter Spaeth
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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 $C^1-$topology. The construction utilizes a continuation argument and chain level result in the Floer theory of Lagrangian intersections.

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Peter Spaeth. 2007-03-25. Length minimizing paths in the Hamiltonian diffeomorphism group. https://arxiv.org/abs/math/0703738

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