Length minimizing paths in the Hamiltonian diffeomorphism group

Details Length minimizing paths in the Hamiltonian diffeomorphism group Length minimizing paths in the Hamiltonian diffeomorphism group

2007-03-25

arxiv.org/abs/math/0703738v2

J. Symplectic Geom. Volume 6, Number 2 (2008), 159-187

Mathematics

Symplectic Geometry

27 pages

Scientific paper

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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