The area preserving Willmore flow and local maximizers of the Hawking mass in asymptotically Schwarzschild manifolds

2018/10/30 by Koerber, Thomas
#35J30 #Differential Geometry (math.DG) #FOS: Mathematics #Primary: 53C20 #Secondary: 83C57

paper · doi:10.48550/arxiv.1810.12866

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 an end is foliated by spheres of Willmore type. 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.

Related

• Large area-constrained Willmore surfaces in asymptotically Schwarzschild 3-manifolds
• Foliations of asymptotically flat manifolds by surfaces of Willmore type
• Local foliations by critical surfaces of the Hawking energy and small sphere limit
• Huisken-Yau-type uniqueness for area-constrained Willmore spheres
• Stability of the area preserving mean curvature flow in asymptotic Schwarzschild space