论文标题
Yamabe指标，Yamabe流的精细解决方案和本地L1稳定性
Yamabe metrics, Fine solutions to the Yamabe flow, and local L1-stability
论文作者
论文摘要
在本文中，我们研究了n维完全的riemannian歧管$（m，g_0）$，$ n \ geq 3 $在n维完全的riemannian歧管上的完全标量曲率的存在。在初始度量的适当条件下，我们表明Yamabe流有一个全球精细的解决方案。这里有趣的观点是，我们没有关于初始度量的曲率假设。我们表明，在n维完整的Riemannian歧管$（M，G_0）$中，具有非负RICCI曲率，$ n \ geq 3 $，Yamabe Flow从多孔媒体方程的视图中享受本地$ l^1 $稳定性属性。还讨论了在N维riemannian模型空间上具有零标量曲率的完整Yamabe指标。
In this paper, we study the existence of complete Yamabe metric with zero scalar curvature on an n-dimensional complete Riemannian manifold $(M,g_0)$, $n\geq 3$. Under suitable conditions about the initial metric, we show that there is a global fine solution to the Yamabe flow. The interesting point here is that we have no curvature assumption about the initial metric. We show that on an n-dimensional complete Riemannian manifold $(M,g_0)$ with non-negative Ricci curvature, $n\geq 3$, the Yamabe flow enjoys the local $L^1$-stability property from the view-point of the porous media equation. Complete Yamabe metrics with zero scalar curvature on an n-dimensional Riemannian model space are also discussed.
