Higher order Willmore hypersurfaces in Euclidean space

DOI10.1007/s10114-008-6422-yzbMath1179.53011OpenAlexW2115760749MaRDI QIDQ1034227

Zhen Guo

Publication date: 11 November 2009

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-008-6422-y

zbMATH Keywords

conformal invariantWillmore hypersurfacehigher-order Willmore functional

Mathematics Subject Classification ID

Global submanifolds (53C40) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

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• A duality theorem for Willmore surfaces
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• Moebius geometry of submanifolds in \(\mathbb{S}^n\)
• Submanifolds with constant Möbius scalar curvature in \(S^n\)
• Möbius geometry of hypersurfaces with constant mean curvature and scalar curvature
• Surfaces with vanishing Möbius form in \(S^n\).
• Willmore submanifolds in a sphere.
• Möbius isoparametric hypersurfaces in \(S^{n+1}\) with two distinct principal curvatures
• Classification of hypersurfaces with parallel Möbius second fundamental form in \(S^{n+1}\)
• Generalized Willmore functionals and related variational problems
• A conformal differential invariant and the conformal rigidity of hypersurfaces
• A Global Invariant of Conformal Mappings in Space
• An Invariant of Conformal Mappings
• The second variational formula for Willmore submanifolds in \(S^n\).
• Conformal geometry of surfaces in \(S^4\) and quaternions

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