Rigidity theorem for Willmore surfaces in a sphere

DOI10.1007/S12044-016-0270-YzbMath1338.53084OpenAlexW2331417714MaRDI QIDQ282329

Dengyun Yang, Hong-Wei Xu

Publication date: 12 May 2016

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-016-0270-y

zbMATH Keywords

mean curvatureWillmore functionalSobolev inequalitytotally umbilical surface

Mathematics Subject Classification ID

Global submanifolds (53C40) Optimization of shapes other than minimal surfaces (49Q10) Rigidity results (53C24)

Related Items (2)

Surface diffusion flow of arbitrary codimension in space forms ⋮ Rigidity of Willmore submanifolds and extremal submanifolds in the unit sphere

Cites Work

• A duality theorem for Willmore surfaces
• Willmore surfaces in \(S^n\)
• Willmore surfaces in the unit \(n\)-sphere
• \(L_{n/2}\)-pinching theorems for submanifolds with parallel mean curvature in a sphere
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• Willmore surfaces on \(\mathbb{R}^4\) and the Whitney sphere
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Rigidity theorem for Willmore surfaces in a sphere