A geometric approach to generalized Stokes conjectures

@article{Varvaruca2009AGA,
  title={A geometric approach to generalized Stokes conjectures},
  author={Eugen Varvaruca and Georg Sebastian Weiss},
  journal={Acta Mathematica},
  year={2009},
  volume={206},
  pages={363-403}
}
We consider the Stokes conjecture concerning the shape of extreme 2-dimensional water waves. By new geometric methods including a non-linear frequency formula, we prove the Stokes conjecture in the original variables. Our results do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity. Part of our results extends to the mathematical problem in higher dimensions. 

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