Minimizers of the Willmore functional with a small area constraint

Details Minimizers of the Willmore functional with a small area constraint Minimizers of the Willmore functional with a small area constraint

2012-01-09

arxiv.org/abs/1201.1887v2

Mathematics

Differential Geometry

Minor corrections

Scientific paper

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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