Abstract
PROPERTIES OF THE GAUSS-GREEN FORM ON THE MODULI SPACE OF UNDULOIDS
FEBRUARY 2008
ELI DAMON, B.E., STATE UNIVERSITY OF NEW YORK AT STONY BROOK
M.S., UNIVERSITY OF MASSACHUSETTS AMHERST
Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST
Directed by: Professor Robert Kusner

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.