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.
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Accepted:
Published online:
Keywords: Willmore surfaces, local foliation
Mot clés : Surface de Willmore, feuilletage local
Lamm, Tobias 1; Metzger, Jan 2; Schulze, Felix 3
@article{AIF_2020__70_4_1639_0, author = {Lamm, Tobias and Metzger, Jan and Schulze, Felix}, title = {Local foliation of manifolds by surfaces of {Willmore} type}, journal = {Annales de l'Institut Fourier}, pages = {1639--1662}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {70}, number = {4}, year = {2020}, doi = {10.5802/aif.3375}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3375/} }
TY - JOUR AU - Lamm, Tobias AU - Metzger, Jan AU - Schulze, Felix TI - Local foliation of manifolds by surfaces of Willmore type JO - Annales de l'Institut Fourier PY - 2020 SP - 1639 EP - 1662 VL - 70 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3375/ DO - 10.5802/aif.3375 LA - en ID - AIF_2020__70_4_1639_0 ER -
%0 Journal Article %A Lamm, Tobias %A Metzger, Jan %A Schulze, Felix %T Local foliation of manifolds by surfaces of Willmore type %J Annales de l'Institut Fourier %D 2020 %P 1639-1662 %V 70 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3375/ %R 10.5802/aif.3375 %G en %F AIF_2020__70_4_1639_0
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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