Willmore 2-Spheres in $$S^n$$ S n : A Survey

DOI10.1007/978-4-431-56021-0_12zbMath1350.53017OpenAlexW2514264157MaRDI QIDQ2819651

Xiang Ma, Peng Wang

Publication date: 29 September 2016

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-4-431-56021-0_12

zbMATH Keywords

minimal surfaceharmonic maploop groupWillmore surfaceDPW methodadjoint transform

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Harmonic maps, etc. (58E20) Optimization of shapes other than minimal surfaces (49Q10) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

Cites Work

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• A duality theorem for Willmore surfaces
• Harmonic maps from surfaces to complex projective spaces
• Spacelike S-Willmore spheres in Lorentzian space forms
• Harmonic maps into Lie groups (classical solutions of the chiral model)
• Weierstrass type representation of harmonic maps into symmetric spaces
• Harmonic two-spheres in compact symmetric spaces, revisited
• Willmore immersions and loop groups
• Conformal geometry of surfaces in Lorentzian space forms
• Minimal immersions of surfaces in Euclidean spheres
• Conformal maps from a 2-torus to the 4-sphere
• Willmore two-spheres in the four-sphere
• A Global Invariant of Conformal Mappings in Space

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