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Journal Article

Foliations of asymptotically flat manifolds by surfaces of Willmore type

MPS-Authors

Lamm,  Tobias
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Metzger,  Jan
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0903.1277
(Preprint), 464KB

277901.pdf
(Any fulltext), 587KB

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Citation

Lamm, T., Metzger, J., & Schulze, F. (2011). Foliations of asymptotically flat manifolds by surfaces of Willmore type. Mathematische Annalen, 350(1), 1-78. doi:10.1007/s00208-010-0550-2.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-6589-4
Abstract
The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with nonzero mass by surfaces which are critical points of the Willmore functional subject to an area constraint. Equivalently these surfaces are critical points of the Geroch-Hawking mass. Thus our result has applications in the theory of General Relativity.