Properties of the Gauss -Green form on the moduli space of unduloids
In this work, we examine the moduli space of unduloids. This space parametrizes the asymptotic behavior of the ends of properly Alexandrov embedded, CMC (constant mean curvature) surfaces of finite topology. In particular, we examine the Gauss-Green form, a natural 2-form on this moduli space. Using coordinate expressions, derived in the appendices, for the Jacobi functions on an unduloid, we derive a coordinate expression for the Gauss-Green form, proving it to be a non-closed, almost-symplectic (i.e. non-degenerate) form. Finally, we outline a path for further study involving the Gromov Compactness Theorem.