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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”.
@article{AIHPC_2019__36_1_181_0,
author = {Chen, Qiyu and Schlenker, Jean-Marc},
title = {Hyperbolic ends with particles and grafting on singular surfaces},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {181--216},
publisher = {Elsevier},
volume = {36},
number = {1},
year = {2019},
doi = {10.1016/j.anihpc.2018.05.001},
mrnumber = {3906870},
zbl = {1408.83030},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.05.001/}
}
TY - JOUR AU - Chen, Qiyu AU - Schlenker, Jean-Marc TI - Hyperbolic ends with particles and grafting on singular surfaces JO - Annales de l'I.H.P. Analyse non linéaire PY - 2019 SP - 181 EP - 216 VL - 36 IS - 1 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.05.001/ DO - 10.1016/j.anihpc.2018.05.001 LA - en ID - AIHPC_2019__36_1_181_0 ER -
%0 Journal Article %A Chen, Qiyu %A Schlenker, Jean-Marc %T Hyperbolic ends with particles and grafting on singular surfaces %J Annales de l'I.H.P. Analyse non linéaire %D 2019 %P 181-216 %V 36 %N 1 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.05.001/ %R 10.1016/j.anihpc.2018.05.001 %G en %F AIHPC_2019__36_1_181_0
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
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