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A geometric approach to generalized Stokes conjectures

Varvaruca, E. and Weiss, G. S. (2011) A geometric approach to generalized Stokes conjectures. Acta Mathematica, 206 (2). pp. 363-403. ISSN 1871-2509

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To link to this item DOI: 10.1007/s11511-011-0066-y


We consider the Stokes conjecture concerning the shape of extreme two-dimensional water waves. By new geometric methods including a nonlinear 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.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:17528
Additional Information:Dedicated to John Toland on the occasion of his 60th birthday.
Publisher Statement:The original publication is available at

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