Foliations of asymptotically flat manifolds by surfaces of Willmore type

TL;DR

This paper proves the existence of a foliation by Willmore-type surfaces in asymptotically flat manifolds, linking geometric analysis with applications in General Relativity.

Contribution

It establishes the existence of a foliation by surfaces critical for the Willmore functional in asymptotically flat manifolds, connecting geometric analysis with gravitational mass concepts.

Findings

Existence of a foliation by Willmore-type surfaces in asymptotically flat manifolds.

Surfaces are critical points of the Geroch-Hawking mass.

Results have implications for the geometric understanding of mass in General Relativity.

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.