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A geometric approach to generalized Stokes conjectures

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Acta Mathematica

Abstract

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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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Reading, Whiteknights, PO Box 220, Reading, RG6 6AX, U.K.

    Eugen Varvaruca

  2. Mathematical Institute, Heinrich Heine University, Universitätsstr. 1, DE-40225, Düsseldorf, Germany

    Georg S. Weiss

Authors
  1. Eugen Varvaruca
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  2. Georg S. Weiss
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Correspondence to Georg S. Weiss.

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Dedicated to John Toland on the occasion of his 60th birthday.

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Varvaruca, E., Weiss, G.S. A geometric approach to generalized Stokes conjectures. Acta Math 206, 363–403 (2011). https://doi.org/10.1007/s11511-011-0066-y

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  • DOI: https://doi.org/10.1007/s11511-011-0066-y

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