Harmonic functions and the mass of 3-dimensional asymptotically flat Riemannian manifolds
Harmonic functions and the mass of 3-dimensional asymptotically flat Riemannian manifolds
复制标题
调和函数和 3 维渐近平坦黎曼流形的质量
DOI：
10.1007/s12220-022-00924-0
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发表时间：
2022
影响因子：
1.1
通讯作者：
Stern, Daniel
中科院分区：
文献类型：
--
作者：
Bray, Hubert;Kazaras, Demetre;Khuri, Marcus;Stern, Daniel
利用线性增长调和函数和标量曲率给出了渐近平坦黎曼三维流形质量的一个显式下界。作为结果，在三维空间中实现了正质量定理的新证明。这个证明与Schoen-Yau最小超曲面技术和Witten的尖刺方法有相似之处。特别地，在Witten的论证中，调和旋量和Richnerowicz公式的作用被调和函数的作用和第四作者在最近的工作中引入的公式所取代，而调和函数的水平集具有类似于Schoen-Yau极小超曲面的作用。
An explicit lower bound for the mass of an asymptotically flat Riemannian 3-manifold is given in terms of linear growth harmonic functions and scalar curvature. As a consequence, a new proof of the positive mass theorem is achieved in dimension three. The proof has parallels with both the Schoen–Yau minimal hypersurface technique and Witten’s spinorial approach. In particular, the role of harmonic spinors and the Lichnerowicz formula in Witten’s argument is replaced by that of harmonic functions and a formula introduced by the fourth named author in recent work, while the level sets of harmonic functions take on a role similar to that of the Schoen–Yau minimal hypersurfaces.