Minimizers of the Willmore functional with a small area constraint
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, pp. 497-518.

We show the existence of a smooth spherical surface minimizing the Willmore functional subject to an area constraint in a compact Riemannian three-manifold, provided the area is small enough. Moreover, we partially classify complete surfaces of Willmore type with positive mean curvature in Riemannian three-manifolds.

DOI : 10.1016/j.anihpc.2012.10.003
Mots-clés : Willmore functional, Minimizers, Direct method 
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Lamm, Tobias; Metzger, Jan. Minimizers of the Willmore functional with a small area constraint. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, pp. 497-518. doi : 10.1016/j.anihpc.2012.10.003. http://www.numdam.org/articles/10.1016/j.anihpc.2012.10.003/

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