Foliations of asymptotically flat manifolds by surfaces of Willmore type
Differential Geometry
2009-03-09 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.0903.1277,
title = {Foliations of asymptotically flat manifolds by surfaces of Willmore type},
author = {Tobias Lamm and Jan Metzger and Felix Schulze},
journal= {arXiv preprint arXiv:0903.1277},
year = {2009}
}
Comments
74 pages