Hyperbolic ends with particles and grafting on singular surfaces
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 181-216.
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We prove that any 3-dimensional 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 3-dimensional 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 Teichmüller 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”.

DOI : 10.1016/j.anihpc.2018.05.001
Mots-clés : Hyperbolic ends, Particles, Complex projective structures, Cone singularities, Constant Gauss curvature, Foliations 
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Chen, Qiyu; Schlenker, Jean-Marc. Hyperbolic ends with particles and grafting on singular surfaces. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 181-216. doi : 10.1016/j.anihpc.2018.05.001. http://www.numdam.org/articles/10.1016/j.anihpc.2018.05.001/

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