For small area-constrained Willmore surfaces, an adapted geometric center of mass satisfies |∇Sc(p0)| ≤ C area, improving the previous C sqrt(area) bound and implying the enclosed region contains a single critical point of scalar curvature.
Local foliation of manifolds by surfaces of Willmore type
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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.
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Refined position estimates for surfaces of Willmore type in Riemannian manifolds
For small area-constrained Willmore surfaces, an adapted geometric center of mass satisfies |∇Sc(p0)| ≤ C area, improving the previous C sqrt(area) bound and implying the enclosed region contains a single critical point of scalar curvature.