## Journal of Differential Geometry

### Quasi-Fuchsian manifolds with particles

#### Abstract

We consider 3-dimensional hyperbolic cone-manifolds which are “convex co-compact” in a natural sense, with cone singularities along infinite lines. Such singularities are sometimes used by physicists as models for massive spinless point particles. We prove an infinitesimal rigidity statement when the angles around the singular lines are less than $\pi$: any infinitesimal deformation changes either these angles, or the conformal structure at infinity with marked points corresponding to the endpoints of the singular lines. Moreover, any small variation of the conformal structure at infinity and of the singular angles can be achieved by a unique small deformation of the cone-manifold structure. These results hold also when the singularities are along a graph, i.e., for “interacting particles”.

#### Article information

Source
J. Differential Geom., Volume 83, Number 1 (2009), 75-129.

Dates
First available in Project Euclid: 24 September 2009

https://projecteuclid.org/euclid.jdg/1253804352

Digital Object Identifier
doi:10.4310/jdg/1253804352

Mathematical Reviews number (MathSciNet)
MR2545031

Zentralblatt MATH identifier
1179.53045

#### Citation

Moroianu, Sergiu; Schlenker, Jean-Marc. Quasi-Fuchsian manifolds with particles. J. Differential Geom. 83 (2009), no. 1, 75--129. doi:10.4310/jdg/1253804352. https://projecteuclid.org/euclid.jdg/1253804352