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Minimal surfaces in germs of hyperbolic 3–manifolds

Clifford Henry Taubes

Geometry & Topology Monographs 7 (2004) 69–100

DOI: 10.2140/gtm.2004.7.69

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 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.

Keywords

hyperbolic 3–manifold, minimal surface

Mathematical Subject Classification

Primary: 53A10, 53C42

Secondary: 53D30

References
Publication

Received: 5 August 2003
Accepted: 21 March 2004
Published: 17 September 2004

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