Hyperbolic ends with particles and grafting on singular surfaces |
| |
Authors: | Qiyu Chen Jean-Marc Schlenker |
| |
Institution: | 1. School of Mathematics, Sun Yat-Sen University, 510275, Guangzhou, PR China;2. Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany;3. University of Luxembourg, UR en Mathématiques, Maison du nombre, 6 avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg |
| |
Abstract: | 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”. |
| |
Keywords: | Hyperbolic ends Particles Complex projective structures Cone singularities Constant Gauss curvature Foliations |
本文献已被 ScienceDirect 等数据库收录! |
|