  Given a surface in an asymptotically flat 3-manifold with nonnegative scalar
curvature, we derive an upper bound for the capacity of the surface in terms of
the area of the surface and the Willmore functional of the surface. The
capacity of a surface is defined to be the energy of the harmonic function
which equals 0 on the surface and goes to 1 at infinity. Even in the special
case of Euclidean space, this is a new estimate. More generally, equality holds
precisely for a spherically symmetric sphere in a spatial Schwarzschild
3-manifold. As applications, we obtain inequalities relating the capacity of
the surface to the Hawking mass of the surface and the total mass of the
asymptotically flat manifold.
