The second variational formula for Willmore submanifolds in \(S^n\).
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Publication:5954152
DOI10.1007/BF03322706zbMath1163.53312MaRDI QIDQ5954152
Haizhong Li, Chang Ping Wang, Zhen Guo
Publication date: 30 January 2002
Published in: Results in Mathematics (Search for Journal in Brave)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A duality theorem for Willmore surfaces
- Hopf tori in \(S^ 3\)
- Inequalities of Willmore type for submanifolds
- Global rigidity theorems of hypersurfaces
- A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
- The conformal Gauss map and the stability of Willmore surfaces
- Hypersurfaces with constant scalar curvature
- Moebius geometry of submanifolds in \(\mathbb{S}^n\)
- Existence of surfaces minimizing the Willmore functional
- Geometrical methods for the elasticity theory of membranes
- Mean Curvature of Riemannian Immersions
- A Moebius characterization of Veronese surfaces in \(S^n\)
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