Ju l 2 00 7 On The Capacity of Surfaces in Manifolds with Nonnegative Scalar Curvature

@inproceedings{Bray2008JuL2,
  title={Ju l 2 00 7 On The Capacity of Surfaces in Manifolds with Nonnegative Scalar Curvature},
  author={Hubert L. Bray and Pengzi Miao},
  year={2008}
}
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 ∞. Even in the special case of R, this is a new estimate. More generally, equality holds precisely for a spherically symmetric sphere in a spatial… CONTINUE READING

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