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We show the existence of a local foliation of a three dimensional Riemannianmanifold by critical points of the Willmore functional subject to a small areaconstraint around non-degenerate critical points of the scalar curvature. Thisadapts a method developed by Rugang Ye to construct foliations by surfaces ofconstant mean curvature.

Local foliation of manifolds by surfaces of Willmore type