论文标题
ADM质量，面积和能力渐近平面$ 3 $ - 具有非负标态曲率的manifolds
ADM mass, area and capacity in asymptotically flat $3$-manifolds with nonnegative scalar curvature
论文作者
论文摘要
我们显示了布雷尖锐的质量容量不等式和Bray-Miao尖锐的尖锐的上限，在其面积方面，边界的容量在其面积方面，对于三维，完整的，一端的渐近歧管，紧凑，连接的边界和非负标度曲率，在拓扑和平均曲率上的适当假设。我们的论点依赖于与歧管边界相关的合适谐波电位的两个单调公式。这项工作是作者博士学位论文中包含的结果的扩展。
We show an improvement of Bray sharp mass-capacity inequality and Bray-Miao sharp upper bound of the capacity of the boundary in terms of its area, for three-dimensional, complete, one-ended asymptotically flat manifolds with compact, connected boundary and with nonnegative scalar curvature, under appropriate assumptions on the topology and on the mean curvature of the boundary. Our arguments relies on two monotonicity formulas holding along level sets of a suitable harmonic potential, associated to the boundary of the manifold. This work is an expansion of the results contained in the PhD thesis of the author.
