Corpus ID: 212725343

Willmore spheres in the 3-sphere revisited

@article{Heller2020WillmoreSI,
  title={Willmore spheres in the 3-sphere revisited},
  author={S. Heller},
  journal={arXiv: Differential Geometry},
  year={2020}
}
  • S. Heller
  • Published 2020
  • Mathematics
  • arXiv: Differential Geometry
  • Bryant \cite{Bryant84} classified all Willmore spheres in $3$-space to be given by minimal surfaces in $\mathbb R^3$ with embedded planar ends. This note provides new explicit formulas for genus 0 minimal surfaces in $\mathbb R^3$ with $2k+1$ embedded planar ends for all $k\geq4.$ Peng and Xiao claimed these examples to exist in \cite{PengXiao2000}, but in the same paper they also claimed the existence of a minimal surface with 7 embedded planar ends, which was falsified by Bryant \cite… CONTINUE READING

    References

    SHOWING 1-7 OF 7 REFERENCES
    The Spinor Representation of Minimal Surfaces
    • 43
    • PDF
    Notes on Projective, Contact, and Null Curves
    • 1
    • PDF
    Surfaces in Conformal Geometry
    • 96
    • Highly Influential
    Willmore Surfaces and Minimal Surfaces with Flat Ends
    • 9
    • Highly Influential
    A duality theorem for Willmore surfaces
    • 345
    • Highly Influential
    Welfengarten 1, 30167 Hannover E-mail address: seb.heller@gmail