Scalar curvature and the relative capacity of geodesic balls
Scalar curvature and the relative capacity of geodesic balls
复制标题
标量曲率和测地球的相对能力
DOI：
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复制
发表时间：
2020
影响因子：
1
通讯作者：
Jeffrey L. Jauregui
中科院分区：
文献类型：
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作者：
Jeffrey L. Jauregui
在黎曼流形中，众所周知，一点处的标量曲率可以从小测地球（球）的体积（面积）中恢复。我们表明，标量曲率同样是由同心小测地球的相对容量。这一结果的动机来自广义相对论（作为对作者以前关于渐近平坦流形中大球容量的研究的补充）和非负标量曲率的弱定义。它还激发了一个猜想（受格雷和范赫克的著名体积猜想的启发），关于小尺度上的相对容量的欧氏行为是否足以表征空间是平坦的。
In a Riemannian manifold, it is well known that the scalar curvature at a point can be recovered from the volumes (areas) of small geodesic balls (spheres). We show the scalar curvature is likewise determined by the relative capacities of concentric small geodesic balls. This result has motivation from general relativity (as a complement to a previous study by the author of the capacity of large balls in an asymptotically flat manifold) and from weak definitions of nonnegative scalar curvature. It also motivates a conjecture (inspired by the famous volume conjecture of Gray and Vanhecke), regarding whether Euclidean-like behavior of the relative capacity on the small scale is sufficient to characterize a space as flat.
DOI：
10.1515/crelle-2019-0040
发表时间：
2018-05
期刊：
Journal für die reine und angewandte Mathematik (Crelles Journal)
影响因子：
--
作者：
Christos Mantoulidis;P. Miao;Luen-Fai Tam
通讯作者：
Christos Mantoulidis;P. Miao;Luen-Fai Tam