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Minimizers of the Willmore functional with a small area constraint

Authors
Journal
Annales de l Institut Henri Poincare (C) Non Linear Analysis
0294-1449
Publisher
Elsevier
Volume
30
Issue
3
Identifiers
DOI: 10.1016/j.anihpc.2012.10.003
Keywords
  • Willmore Functional
  • Minimizers
  • Direct Method

Abstract

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.

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