  We show, using strong subadditivity and Lorentz covariance, that in three
dimensional space-time the entanglement entropy of a circle is a concave
function. This implies the decrease of the coefficient of the area term and the
increase of the constant term in the entropy between the ultraviolet and
infrared fixed points. This is in accordance with recent holographic c-theorems
and with conjectures about the renormalization group flow of the partition
function of a three sphere (F-theorem). The irreversibility of the
renormalization group flow in three dimensions would follow from the argument
provided there is an intrinsic definition for the constant term in the entropy
at fixed points. We discuss the difficulties in generalizing this result for
spheres in higher dimensions.
