Foliations of asymptotically flat manifolds by surfaces of Willmore type

2009/03/06 by Lamm, Tobias, Metzger, Jan, Schulze, Felix · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0903.1277

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.

Cited by

• Foliations by critical surfaces of the Hawking energy in asymptotically flat initial data sets
• Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces

Related

• Local foliation of manifolds by surfaces of Willmore type
• The area preserving Willmore flow and local maximizers of the Hawking mass in asymptotically Schwarzschild manifolds
• Local foliations by critical surfaces of the Hawking energy and small sphere limit
• Large area-constrained Willmore surfaces in asymptotically Schwarzschild 3-manifolds
• Foliation by Constant Mean Curvature Spheres on Asymptotically Flat Manifolds