Local foliation of manifolds by surfaces of Willmore type
Annales de l'Institut Fourier, Volume 70 (2020) no. 4, pp. 1639-1662.

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.

Nour prouvons l’existence d’un feuilletage local d’une variété riemanienne de dimension trois autour des points critiques de la courbure scalaire par les points critiques non dégénérés de la fonctionnelle de Willmore sous la contrainte d’aire petite. On adapte une méthode développée par Rugang Ye pour construire un feuilletage par des surfaces à courbure moyenne constante.

Published online:
DOI: 10.5802/aif.3375
Classification: 53A30, 53C40
Keywords: Willmore surfaces, local foliation
Lamm, Tobias 1; Metzger, Jan 2; Schulze, Felix 3

1 Karlsruhe Institute of Technology Institute for Analysis Englerstrasse 2 76131 Karlsruhe (Germany)
2 University of Potsdam Institute for Mathematics Karl-Liebknecht-Straße 24/25 14476 Potsdam (Germany)
3 Department of Mathematics University College London 25 Gordon St. London WC1E 6BT (UK)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Local foliation of manifolds by surfaces of {Willmore} type},
     journal = {Annales de l'Institut Fourier},
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     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Lamm, Tobias; Metzger, Jan; Schulze, Felix. Local foliation of manifolds by surfaces of Willmore type. Annales de l'Institut Fourier, Volume 70 (2020) no. 4, pp. 1639-1662. doi : 10.5802/aif.3375. https://aif.centre-mersenne.org/articles/10.5802/aif.3375/

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