Willmore surfaces on \(\mathbb{R}^4\) and the Whitney sphere

DOI10.1023/A:1010720100464zbMath0991.53039OpenAlexW165666246MaRDI QIDQ5936999

Francisco Urbano, Ildefonso Castro

Publication date: 12 July 2001

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1010720100464

zbMATH Keywords

Lagrangian submanifoldWhitney sphereWillmore surface

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Variational problems in infinite-dimensional spaces (58E99)

Related Items (16)

Rigidity theorem for Willmore surfaces in a sphere ⋮ Willmore-like tori in Killing submersions ⋮ On Willmore Legendrian surfaces in \(\mathbb S^5\) and the contact stationary Legendrian Willmore surfaces ⋮ An energy gap phenomenon for the Whitney sphere ⋮ A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves ⋮ On energy gap phenomena of the Whitney spheres in \(\mathbb{C}^n\) or \(\mathbb{CP}^n\) ⋮ Rigidity of Willmore submanifolds and extremal submanifolds in the unit sphere ⋮ On energy gap phenomena of the Whitney sphere and related problems ⋮ Complete Willmore Legendrian surfaces in \(\mathbb{S}^5\) are minimal Legendrian surfaces ⋮ Normal critical surfaces in \(\mathbb{C}P^2\) ⋮ A Helfrich functional for compact surfaces in ⋮ Surfaces with vanishing Möbius form in \(S^n\). ⋮ Lagrangian surfaces in complex Euclidean plane via spherical and hyperbolic curves ⋮ A note on the evolution of the Whitney sphere Along mean curvature flow ⋮ Lagrangian surfaces with Legendrian boundary ⋮ New characterizations of the Whitney spheres and the contact Whitney spheres

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