Length minimizing paths in the Hamiltonian diffeomorphism group
Spaeth, Peter W.
J. Symplectic Geom., Tome 6 (2008) no. 2, p. 159-187 / Harvested from Project Euclid
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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.
Publié le : 2008-06-15
Classification:  
@article{1219866511,
     author = {Spaeth, Peter W.},
     title = {Length minimizing paths in the Hamiltonian diffeomorphism group},
     journal = {J. Symplectic Geom.},
     volume = {6},
     number = {2},
     year = {2008},
     pages = { 159-187},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1219866511}
}

Spaeth, Peter W. Length minimizing paths in the Hamiltonian diffeomorphism group. J. Symplectic Geom., Tome 6 (2008) no. 2, pp.  159-187. http://gdmltest.u-ga.fr/item/1219866511/