# Minimal surfaces and particles in 3-manifolds

@article{Krasnov2007MinimalSA, title={Minimal surfaces and particles in 3-manifolds}, author={Kirill Krasnov and Jean-Marc Schlenker}, journal={Geometriae Dedicata}, year={2007}, volume={126}, pages={187-254} }

We consider 3-dimensional anti-de Sitter manifolds with conical singularities along time-like lines, which is what in the physics literature is known as manifolds with particles. We show that the space of such cone-manifolds is parametrized by the cotangent bundle of Teichmüller space, and that moreover such cone-manifolds have a canonical foliation by space-like surfaces. We extend these results to de Sitter and Minkowski cone-manifolds, as well as to some related “quasifuchsian” hyperbolic…

## 106 Citations

Quasi-Fuchsian manifolds with particles

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We consider 3-dimensional hyperbolic cone-manifolds which are “convex cocompact” in a natural sense, with cone singularities along infinite lines. Such singularities are sometimes used by physicists…

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In the former articles [17; 31], it was independently proven by the authors that the space of hyperbolic cone‐3‐manifolds with cone angles less than 2 and fixed singular locus is locally parametrized…

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The renormalized volume of hyperbolic manifolds is a quantity motivated by the AdS/CFT correspondence of string theory and computed via a certain regularization procedure. The main aim of the present…

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We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are " convex co-compact " in a natural sense. We prove an infinitesimal rigidity statement when the angle…

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