JournalsaihpcVol. 30, No. 3pp. 497–518

Minimizers of the Willmore functional with a small area constraint

  • Tobias Lamm

    Goethe-Universität Frankfurt, Institut für Mathematik, Robert-Mayer-Str. 10, 60054 Frankfurt, Germany, Institute for Analysis, Karlsruhe Institute of Technology (KIT), Kaiserstr. 89, 76128 Karlsruhe, Germany

  • Jan Metzger

    Universität Potsdam, Institut für Mathematik, Am Neuen Palais 10, 14469 Potsdam, Germany
Minimizers of the Willmore functional with a small area constraint cover
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Abstract

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.

Cite this article

Tobias Lamm, Jan Metzger, Minimizers of the Willmore functional with a small area constraint. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 3, pp. 497–518

DOI 10.1016/J.ANIHPC.2012.10.003