A geometric approach to generalized Stokes conjectures

Eugen Varvaruca; Georg S. Weiss

doi:10.1007/s11511-011-0066-y

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Home > Journals > Acta Math. > Volume 206 > Issue 2 > Article

2011 A geometric approach to generalized Stokes conjectures

Eugen Varvaruca, Georg S. Weiss

Author Affiliations +

Eugen Varvaruca,¹ Georg S. Weiss²
¹Department of Mathematics and Statistics, University of Reading
²Mathematical Institute, Heinrich Heine University

Acta Math. 206(2): 363-403 (2011). DOI: 10.1007/s11511-011-0066-y

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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.

Dedication

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

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Eugen Varvaruca. Georg S. Weiss. "A geometric approach to generalized Stokes conjectures." Acta Math. 206 (2) 363 - 403, 2011. https://doi.org/10.1007/s11511-011-0066-y