  We use the criteria of Lalonde and McDuff to show that a path that is
generated by a generic autonomous Hamiltonian is length minimizing with respect
to the Hofer norm among all homotopic paths provided that it induces no
non-constant closed trajectories in M. This generalizes a result of Hofer for
symplectomorphisms of Euclidean space. The proof for general M uses Liu-Tian's
construction of S^1-invariant virtual moduli cycles. As a corollary, we find
that any semifree action of S^1 on M gives rise to a nontrivial element in the
fundamental group of the symplectomorphism group of M. We also establish a
version of the area-capacity inequality for quasicylinders.
