  In axially symmetric spacetimes the Penrose inequality can be strengthened to
include angular momentum. We prove a version of this inequality for minimal
surfaces, more precisely, a lower bound for the ADM mass in terms of the area
of a minimal surface, the angular momentum and a particular measure of the
surface size. We consider axially symmetric and asymptotically flat initial
data, and use the monotonicity of the Geroch quasi-local energy on 2-surfaces
along the inverse mean curvature flow.
