Minimizers of the Willmore functional with a small area constraint
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, p. 497-518
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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.
@article{AIHPC_2013__30_3_497_0,
     author = {Lamm, Tobias and Metzger, Jan},
     title = {Minimizers of the Willmore functional with a small area constraint},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {30},
     number = {3},
     year = {2013},
     pages = {497-518},
     doi = {10.1016/j.anihpc.2012.10.003},
     zbl = {1290.49090},
     language = {en},
     url = {http://http://www.numdam.org/item/AIHPC_2013__30_3_497_0}
}
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/item/AIHPC_2013__30_3_497_0/

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