We study the infinitesimal aspects of the following problem. Let H be a
Hamiltonian of \R^{2n} whose energy surface {H=1} encloses a compact starshaped
domain of volume equal to that of the unit ball in \R^{2n}. Does the energy
surface {H=1} carry a periodic orbit of the Hamiltonian system associated to H
with action less than or equal to \pi ?