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.

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Clifford Henry Taubes
Department of Mathematics, Harvard University
Cambridge, MA 02138, USA

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