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Local foliation of manifolds by surfaces of Willmore type

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arxiv 1806.00465 v2 pith:C3PIM753 submitted 2018-06-01 math.DG

Tobias Lamm , Jan Metzger , Felix Schulze This is my paper · ORCID
classification math.DG
keywords criticalcurvaturefoliationlocalpointssurfaceswillmoreadapts
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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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  1. Refined position estimates for surfaces of Willmore type in Riemannian manifolds

    math.DG 2019-08 conditional novelty 6.0 of 10

    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 poi...

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