Quasi-fuchsian manifolds with particles

Sergiu Moroianu Institutul de Matematic˘a al Academiei Romˆane Jean-Marc Schlenker Universit´e Paul Sabatier

Differential Geometry mathscidoc:1609.10134

Journal of Differential Geometry, 83, (1), 75-129, 2009
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 π: 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”.
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@inproceedings{sergiu2009quasi-fuchsian,
  title={QUASI-FUCHSIAN MANIFOLDS WITH PARTICLES},
  author={Sergiu Moroianu, and Jean-Marc Schlenker},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911195121783910791},
  booktitle={Journal of Differential Geometry},
  volume={83},
  number={1},
  pages={75-129},
  year={2009},
}
Sergiu Moroianu, and Jean-Marc Schlenker. QUASI-FUCHSIAN MANIFOLDS WITH PARTICLES. 2009. Vol. 83. In Journal of Differential Geometry. pp.75-129. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911195121783910791.
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