We study the area preserving Willmore flow in an asymptotic region of an asymptotically flat manifold which is \(C^3\)-close to Schwarzschild. It was shown by Lamm, Metzger and Schulze that such a region is foliated by spheres of Willmore type, see (Lamm et al. in Math Ann 350(1):1–78, 2011). In this paper, we prove that the leaves of this foliation are stable under small area preserving \(W^{2,2}\)-perturbations with respect to the area preserving Willmore flow. This implies, in particular, that the leaves are strict local area preserving maximizers of the Hawking mass with respect to the \(W^{2,2}\)-topology.

我们研究了渐近平坦流形的渐近区域中保卫Willmore流的区域，该渐近区域是\（C ^ 3 \）-接近Schwarzschild。Lamm，Metzger和Schulze指出，这样的区域被Willmore类型的球体所遮盖，请参阅（Lamm等人，Math Ann 350（1）：1-78，2011年）。在本文中，我们证明了该叶的叶子在相对于保留Willmore流量的小面积保持\（W ^ {2,2} \）-扰动下是稳定的。特别地，这意味着，叶子是严格的局部区域，相对于\（W ^ {2,2} \）-拓扑，保留了霍金质量的最大化。