Unstable CMC spheres and outlying CMC spheres in AF 3-manifolds

作者：Ma, Shiguang^*

来源：Communications in Contemporary Mathematics, 2018, 20(1): 1650065.

DOI：10.1142/S0219199716500656

• Asymptotically flat manifold
• constant mean curvature
• unstable
• outlying

In this paper, we introduce a nonlinear ODE method to construct constant mean curvature (CMC) surfaces in Riemannian manifolds with symmetry. As an application, we construct unstable CMC spheres and outlying CMC spheres in asymptotically Schwarzschild manifolds with metrics like g(ij) = (1+ 1/l)(2)delta(ij) + O(l(-2)). The existence of unstable CMC spheres tells us that the stability condition in Qing-Tian's work [On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds, J. Amer. Math. Soc. 20(4) (2007) 1091-1110] cannot be removed generally.

• 出版日期2018-2
• 单位南开大学