#### Geometry & Topology Monographs, Vol. 7 (2004),

Proceedings of the Casson Fest,

Paper no. 3, pages 69--100.

## Minimal surfaces in germs of hyperbolic 3-manifolds

### Clifford Henry Taubes

**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.
**Keywords**.
Hyperbolic 3-manifold, minimal surface

**AMS subject classification**.
Primary: 53C42, 53A10.
Secondary: 53D30.

**E-print:** `arXiv:math.GT/0410326`

Submitted to GT on 5 August 2003.
Paper accepted 21 March 2004.
Paper published 17 September 2004.

Notes on file formats
Clifford Henry Taubes

Department of Mathematics, Harvard University

Cambridge, MA 02138, USA

Email: chtaubes@math.harvard.edu

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