arXiv:0908.1031 Abstract | arXiv Analytics

arXiv:0908.1031 [math.AP]Abstract References Reviews Resources

A geometric approach to generalized Stokes conjectures

Published 2009-08-07, updated 2010-04-27Version 2

We consider Stokes' conjecture concerning the shape of the extremal two-dimensional water wave. By new geometric methods including a nonlinear frequency formula, we prove 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.

Comments: accepted for publication in Acta Mathematica; 39 pages, 1 figure

Categories: math.AP

Subjects: 35R35, 76B15, 76B07

Keywords: generalized stokes conjectures, geometric approach, extremal two-dimensional water wave, nonlinear frequency formula, geometric methods

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