Symmetric doubly periodic gravity-capillary waves with small vorticity
We construct small amplitude gravity-capillary water waves with small nonzero vorticity, in three spatial dimensions, bifurcating from uniform flows. The waves are symmetric, and periodic in both horizontal coordinates. The proof is inspired by Lortz' construction of magnetohydrostatic equilibria in reflection-symmetric toroidal domains. It relies on a representation of the vorticity as the cross