Given a constant mean curvature surface that bounds a compact manifold with nonnegative scalar curvature, we obtain intrinsic conditions on the surface that guarantee the positivity of its Hawking mass. We also obtain estimates of the Bartnik mass of such surfaces, without assumptions on the integral of the squared mean curvature. If the ambient manifold has negative scalar curvature, our method also applies and yields estimates on the hyperbolic Bartnik mass of these surfaces.

中文翻译：

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关于 CMC 表面的霍金质量和巴特尼克质量

给定一个恒定的平均曲率表面，该表面以非负标量曲率限定紧凑流形，我们在表面上获得了保证其霍金质量为正的内在条件。我们还获得了此类表面的 Bartnik 质量的估计值，而无需对平方平均曲率的积分进行假设。如果环境流形具有负标量曲率，我们的方法也适用并产生对这些表面的双曲 Bartnik 质量的估计。