Reference : Hyperbolic ends with particles and grafting on singular surfaces
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Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
http://hdl.handle.net/10993/33901
Hyperbolic ends with particles and grafting on singular surfaces
English
chen, qiyu []
Schlenker, Jean-Marc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Apr-2017
No
[en] hyperbolic ; lorentzian ; particles
[en] We prove that any hyperbolic end with particles (cone singularities along infinite curves of angles less than π) admits a unique foliation by constant Gauss curvature surfaces. Using a form of duality between hyperbolic ends with particles and convex globally hyperbolic maximal (GHM) de Sitter spacetime with particles, it follows that any convex GHM de Sitter spacetime with particles also admits a unique foliation by constant Gauss curvature surfaces. We prove that the grafting map from the product of Teichm\"uller space with the space of measured laminations to the space of complex projective structures is a homeomorphism for surfaces with cone singularities of angles less than π, as well as an analogue when grafting is replaced by "smooth grafting".
http://hdl.handle.net/10993/33901
https://arxiv.org/abs/1704.07167

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