For CMC surfaces in 3-dimensional space forms, we relate the moment class of Korevaar–Kusner–Solomon to a second cohomology class arising from the integrable systems theory of isothermic surfaces. In addition, we show that both classes have a variational origin as Noether currents.

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Isothermic Surfaces and Conservation Laws

  • Fran Burstall,
  • Emma Carberry,
  • Udo Hertrich-Jeromin,
  • Franz Pedit

摘要

For CMC surfaces in 3-dimensional space forms, we relate the moment class of Korevaar–Kusner–Solomon to a second cohomology class arising from the integrable systems theory of isothermic surfaces. In addition, we show that both classes have a variational origin as Noether currents.