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Minimizers of the willmore functional with a small area constraint
- 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.
Author details: | Tobias Lamm, Jan Metzger |
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DOI: | https://doi.org/10.1016/j.anihpc.2012.10.003 |
ISSN: | 0294-1449 |
Title of parent work (English): | ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE |
Publisher: | Elsevier |
Place of publishing: | Paris |
Publication type: | Article |
Language: | English |
Year of first publication: | 2013 |
Publication year: | 2013 |
Release date: | 2017/03/26 |
Tag: | Direct method; Minimizers; Willmore functional |
Volume: | 30 |
Issue: | 3 |
Number of pages: | 22 |
First page: | 497 |
Last Page: | 518 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |