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The closure of spectral data for constant mean curvature tori in 𝕊3

  • Emma Carberry EMAIL logo and Martin Ulrich Schmidt
Published/Copyright: August 31, 2014
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Journal für die reine und angewandte Mathematik (Crelles Journal)
From the journal Journal für die reine und angewandte Mathematik (Crelles Journal) Volume 2016 Issue 721

Abstract

The spectral curve correspondence for finite-type solutions of the sinh- Gordon equation describes how they arise from and give rise to hyperelliptic curves with a real structure. Constant mean curvature (CMC) 2-tori in 𝕊3 result when these spectral curves satisfy periodicity conditions. We prove that the spectral curves of CMC tori are dense in the space of smooth spectral curves of finite-type solutions of the sinh-Gordon equation. One consequence of this is the existence of countably many real n-dimensional families of CMC tori in 𝕊3 for each positive integer n.

References

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Received: 2013-8-29
Published Online: 2014-8-31
Published in Print: 2016-12-1

© 2016 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Singularities with 𝔾m-action and\break the log minimal model program for ℳ¯g
  3. Normal functions, Picard--Fuchs equations, and elliptic fibrations on K3 surfaces
  4. Degrees of strongly special subvarieties and the André–Oort conjecture
  5. Ambitoric geometry I: Einstein metrics and extremal ambikähler structures
  6. The closure of spectral data for constant mean curvature tori in 𝕊3
  7. Modular p-adic L-functions attached to real quadratic fields and arithmetic applications
  8. Dimension invariants for groups admitting a cocompact model for proper actions
https://doi.org/10.1515/crelle-2014-0068

Articles in the same Issue

  1. Frontmatter
  2. Singularities with 𝔾m-action and\break the log minimal model program for ℳ¯g
  3. Normal functions, Picard--Fuchs equations, and elliptic fibrations on K3 surfaces
  4. Degrees of strongly special subvarieties and the André–Oort conjecture
  5. Ambitoric geometry I: Einstein metrics and extremal ambikähler structures
  6. The closure of spectral data for constant mean curvature tori in 𝕊3
  7. Modular p-adic L-functions attached to real quadratic fields and arithmetic applications
  8. Dimension invariants for groups admitting a cocompact model for proper actions
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