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<p>The purpose of this work is to establish an upper bound for the capacity of the surface in a three-dimensional asymptotically flat half-space with nonnegative scalar curvature and mean convex boundary. If the equality holds, we show a rigidity result involving the half-Schwarzschild space. In order to prove our result we use the inverse of mean curvature flow for hypersurfaces with boundary.</p>

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On the capacity of surfaces in asymptotically flat half-space

  • 期刊论文

  • 发表日期：

    2025年4月21日

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  • Daniel Silva

摘要

The purpose of this work is to establish an upper bound for the capacity of the surface in a three-dimensional asymptotically flat half-space with nonnegative scalar curvature and mean convex boundary. If the equality holds, we show a rigidity result involving the half-Schwarzschild space. In order to prove our result we use the inverse of mean curvature flow for hypersurfaces with boundary.