从2维到7维中ADM质量的下半连续性
Lower semicontinuity of the ADM mass in dimensions two through seven
摘要：
ADM质量在尖点（即，渐近平坦度规的局部收敛是一个有趣的问题，因为它与非负数量曲率、正质量定理和广义相对论中的Bartnik质量最小化问题有关。本文利用S. McCormick和P.Miao（它本身建立在H. Bray和D. Lee）。由于技术上的原因，我们限制到极限空间是渐近史瓦西的情况。在一个单独的结果，我们表明，连续性持有加权下，而不是指出，$C^2$收敛，在所有维度$n \geq 3$，一个简单的证明独立的正质量定理。最后，我们还解决了二维情况下的点收敛，其中的渐近锥面角假设的ADM质量的作用。
英文摘要：
The semicontinuity phenomenon of the ADM mass under pointed (i.e., local) convergence of asymptotically flat metrics is of interest because of its connections to nonnegative scalar curvature, the positive mass theorem, and Bartnik's mass-minimization problem in general relativity. In this paper, we extend a previously known semicontinuity result in dimension three for $C^2$ pointed convergence to higher dimensions, up through seven, using recent work of S. McCormick and P. Miao (which itself builds on the Riemannian Penrose inequality of H. Bray and D. Lee). For a technical reason, we restrict to the case in which the limit space is asymptotically Schwarzschild. In a separate result, we show that semicontinuity holds under weighted, rather than pointed, $C^2$ convergence, in all dimensions $n \geq 3$, with a simpler proof independent of the positive mass theorem. Finally, we also address the two-dimensional case for pointed convergence, in which the asymptotic cone angle assumes the role of the ADM mass.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
