论文标题
$ c^0 $ c^0 $度量和失真下的质量
ADM mass for $C^0$ metrics and distortion under Ricci-DeTurck flow
论文作者
论文摘要
我们表明，存在一个数量，仅取决于$ c^0 $的riemannian度量数据，每当AMD质量存在时，它与通常的ADM质量一致，但在无穷大的限制中，对于任何连续的Riemannian量都有明确的限制，对于任何连续的Riemannian度量，它们在$ C^0 $ sense and sense and sense and nosecation Curverci curverci curvercici curverci curverci curvip curvip curvial中均不含。此外，Infinity的$ c^0 $质量独立于$ C^0 $ - 偶然平坦的坐标图的选择，而$ C^0 $本地质量在Ricci-deturck流量下与合适发展的测试功能相连时，在Ricci-deturck流量下控制了失真。
We show that there exists a quantity, depending only on $C^0$ data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the $C^0$ sense and has nonnegative scalar curvature in the sense of Ricci flow. Moreover, the $C^0$ mass at infinity is independent of choice of $C^0$-asymptotically flat coordinate chart, and the $C^0$ local mass has controlled distortion under Ricci-DeTurck flow when coupled with a suitably evolving test function.
