Minimal surfaces in germs of hyperbolic 3--manifolds

Details Minimal surfaces in germs of hyperbolic 3--manifolds Minimal surfaces in germs of hyperbolic 3--manifolds

2004-10-13

arxiv.org/abs/math/0410326v1

Geom. Topol. Monogr. 7 (2004) 69-100

Mathematics

Geometric Topology

Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper3.abs.html

Scientific paper

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.

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