The area preserving Willmore flow and local maximizers of the Hawking mass in asymptotically Schwarzschild manifolds
Abstract: We study the area preserving Willmore flow in an asymptotic region of an asymptotically flat manifold which is C3-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 W2,2-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 W2,2-topology
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Notes
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The journal of geometric analysis. - 31, 4 (2021) , 3455-3497, ISSN: 1559-002X
- DOI
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10.1007/s12220-020-00401-6
- URN
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urn:nbn:de:bsz:25-freidok-1949443
- Rights
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Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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25.03.2025, 1:54 PM CET
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Associated
- Körber, Thomas
- Universität
Time of origin
- 2021
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