Displaying similar documents to “Hofer-Zehnder capacity and length minimizing Hamiltonian paths.”

Length minimizing Hamiltonian paths for symplectically aspherical manifolds

Ely Kerman, François Lalonde (2003)

Annales de l’institut Fourier

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In this note we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of Polterovich and Schwarz, we study the role, in the Floer complex of the generating Hamiltonian, of the global extrema which remain fixed as the time varies. Our main result determines a natural condition which implies that the corresponding path minimizes the positive Hofer length. We use this to prove...