Minimal surfaces in germs of hyperbolic 3--manifolds

Abstract

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 Teichmueller space and the space of SO(3,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.