Journal of Symplectic Geometry

Length minimizing paths in the Hamiltonian diffeomorphism group

Peter W. 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.

Article information

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

Dates
First available in Project Euclid: 27 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1219866511

Mathematical Reviews number (MathSciNet)
MR2434439

Zentralblatt MATH identifier
1151.53072

Citation

Spaeth, Peter W. Length minimizing paths in the Hamiltonian diffeomorphism group. J. Symplectic Geom. 6 (2008), no. 2, 159--187. https://projecteuclid.org/euclid.jsg/1219866511


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