Hyperbolic ends with particles and grafting on singular surfaces

Chen, Qiyu; Schlenker, Jean-Marc

doi:10.1016/j.anihpc.2018.05.001

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Hyperbolic ends with particles and grafting on singular surfaces

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Chen, Qiyu
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.anihpc.2018.05.001
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Chen-Schlenker_Hyperbolic ends with particles and grafting on singular surfaces_oa_2019.pdf
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Citation

Chen, Q., & Schlenker, J.-M. (2019). Hyperbolic ends with particles and grafting on singular surfaces. Annales DE l'Institut Henri Poincare C, Analyse Non Lineaire, 36(1), 181-216. doi:10.1016/j.anihpc.2018.05.001.

Cite as: https://hdl.handle.net/21.11116/0000-0004-411D-3

Abstract

We prove that any 3-dimensional hyperbolic end with particles (cone singularities along infinite curves of anglesless than \pi) 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 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 \pi, as well as an analogue when grafting is replaced by “smooth grafting”.