Abstract
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.
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