This article introduces a universal moduli space for the set whose
archetypal element is a pair that consists of a metric and second
fundamental form from a compact, oriented, positive genus minimal surface
in some hyperbolic 3–manifold. This moduli space is a smooth, finite
dimensional manifold with canonical maps to both the cotangent bundle
of the Teichmüller space and the space of SO3(C)
representations for the given genus surface. These two maps embed the
universal moduli space as a Lagrangian submanifold in the product of
the latter two spaces.
