论文标题
通过稳定的常数平均曲率球的渐近平坦3型体的叶子
Foliations of asymptotically flat 3-manifolds by stable constant mean curvature spheres
论文作者
论文摘要
令$（m，g）$为渐近平坦的riemannian dimension $ n \ geq 3 $，具有正质量。我们通过稳定的常数均值曲率球的渐近叶（m，g）$降低了$（m，g）$的渐近叶子的存在，提供了一个简短的证明。此外，我们表明，叶片的质量几何中心与$（m，g）$的汉密尔顿弥撒中心一致。在尺寸$ n = 3 $中，C. nerz先前使用其他方法显示了这些结果。如果$ n = 3 $和$（m，g）$的标量曲率是非负数的，那么我们证明渐近叶叶的叶子是唯一包围$（m，g）$中心的唯一大稳定常数平均曲率球。以前在更限制的衰减假设和S. ma使用其他方法中显示了这一点。
Let $(M,g)$ be an asymptotically flat Riemannian manifold of dimension $n\geq 3$ with positive mass. We give a short proof based on Lyapunov-Schmidt reduction of the existence of an asymptotic foliation of $(M, g)$ by stable constant mean curvature spheres. Moreover, we show that the geometric center of mass of the foliation agrees with the Hamiltonian center of mass of $(M,g)$. In dimension $n = 3$, these results were shown previously by C. Nerz using a different approach. In the case where $n=3$ and the scalar curvature of $(M, g)$ is nonnegative, we prove that the leaves of the asymptotic foliation are the only large stable constant mean curvature spheres that enclose the center of $(M, g)$. This was shown previously under more restrictive decay assumptions and using a different method by S. Ma.
