Local foliation of manifolds by surfaces of Willmore type

Abstract

We show the existence of a local foliation of a three dimensional Riemannian manifold by critical points of the Willmore functional subject to a small area constraint around non-degenerate critical points of the scalar curvature. This adapts a method developed by Rugang Ye to construct foliations by surfaces of constant mean curvature.

arXiv commentMinor modifications, to appear in Ann. Inst. Fourier (Grenoble)