  An area-preserving diffeomorphism of an annulus has an "action function"
which measures how the diffeomorphism distorts curves. The average value of the
action function over the annulus is known as the Calabi invariant of the
diffeomorphism, while the average value of the action function over a periodic
orbit of the diffeomorphism is the mean action of the orbit. If an
area-preserving annulus diffeomorphism is a rotation near the boundary of the
annulus, and if its Calabi invariant is less than the maximum boundary value of
the action function, then we show that the infimum of the mean action over all
periodic orbits of the diffeomorphism is less than or equal to its Calabi
invariant.
