• Sebastian Klein
Part of the Lecture Notes in Mathematics book series (LNM, volume 2229)


In this book we studied (singularity-free) simply periodic solutions \(u:X \to \mathbb {C}\) of the sinh-Gordon equation via their spectral data (Σ, D) in the style of Bobenko. In particular we gained insight into the asymptotic behavior of the spectral data. As we saw in Chap.  2, real-valued such solutions give rise to minimal immersions f : X → S3, and similarly to constant mean curvature (CMC) immersions into \(\mathbb {R}^3\) and H3. In this situation, umbilical points of the immersion correspond to coordinate singularities of the solution u. In the following, I sketch how the research described in this book might be extended to solutions u with such coordinate singularities, and why the corresponding minimal immersions with umbilical points are of interest.


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Authors and Affiliations

  • Sebastian Klein
    • 1
  1. 1.School of Business Informatics & MathematicsUniversity of MannheimMannheimGermany

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