For small angular momentum, there exists a unique rotation orbit of smooth rotating capillary drop solutions near the circle, built by a variational bifurcation argument from a multiple eigenvalue.
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Two-dimensional capillary liquid drop: Craig-Sulem formulation on $\mathbb{T}^1$ and bifurcations from multiple eigenvalues of rotating waves
For small angular momentum, there exists a unique rotation orbit of smooth rotating capillary drop solutions near the circle, built by a variational bifurcation argument from a multiple eigenvalue.