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The Area Preserving Willmore Flow and Local Maximizers of the Hawking Mass in Asymptotically Schwarzschild Manifolds
The Journal of Geometric Analysis ( IF 0.924 ) Pub Date : 2020-04-10 , DOI: 10.1007/s12220-020-00401-6
Thomas Koerber

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.
更新日期:2020-04-10

 

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