Startseite The closure of spectral data for constant mean curvature tori in đť•Š3
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The closure of spectral data for constant mean curvature tori in đť•Š3

  • Emma Carberry EMAIL logo und Martin Ulrich Schmidt
Veröffentlicht/Copyright: 31. August 2014
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Journal fĂĽr die reine und angewandte Mathematik (Crelles Journal)
Aus der Zeitschrift Journal fĂĽr die reine und angewandte Mathematik (Crelles Journal) Band 2016 Heft 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 đť•Š3 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 đť•Š3 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

Artikel in diesem Heft

  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 đť•Š3
  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

Artikel in diesem Heft

  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 đť•Š3
  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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