Corpus ID: 212725343

Willmore spheres in the 3-sphere revisited

  title={Willmore spheres in the 3-sphere revisited},
  author={S. Heller},
  journal={arXiv: Differential Geometry},
  • 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


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