渐近Schwarzschild流形中的面积保持Willmore流和Hawking质量的局部极大化
The area preserving Willmore flow and local maximizers of the Hawking mass in asymptotically Schwarzschild manifolds
摘要：
本文研究了渐近平坦流形上$C^{3}-$接近Schwarzschild的渐近区域中的保面积Willmore流。拉姆、梅茨格和舒尔策指出，这种端部是由威尔莫尔型球体形成的。在本文中，我们证明了这个叶理的叶子是稳定的小面积保持$W^{2,2}-$扰动下的面积保持Willmore流。这意味着，特别是，叶子是严格的局部面积保持最大化的霍金质量相对于$W^{2,2}-$拓扑结构。
英文摘要：
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 an end is foliated by spheres of Willmore type. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
