Minimizers of the Willmore functional with a small area constraint

Tobias Lamm; Jan Metzger

doi:10.1016/j.anihpc.2012.10.003

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arXiv · 1201.1887

Minimizers of the Willmore functional with a small area constraint

Tobias Lamm·Jan Metzger

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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 classify complete surfaces of Willmore type with positive mean curvature in Riemannian three-manifolds.

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Tobias Lamm, Jan Metzger. 2012-01-09. Minimizers of the Willmore functional with a small area constraint. https://doi.org/10.1016/j.anihpc.2012.10.003

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