Constant Gauss curvature foliations of AdS spacetimes with particles
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- by Qiyu Chen and Jean-Marc Schlenker PDF
- Trans. Amer. Math. Soc. 373 (2020), 4013-4049 Request permission
Abstract:
We prove that for any convex globally hyperbolic compact maximal (GHCM) anti-de Sitter (AdS) 3-dimensional spacetime $N$ with particles (cone singularities of angles less than $\pi$ along time-like lines), the complement of the convex core in $N$ admits a unique foliation by constant Gauss curvature surfaces. This extends and provides a new proof of a result of Barbot, Béguin, and Zeghib. We also describe a parametrization of the space of convex GHCM AdS metrics on a given manifold, with particles of given angles, by the product of two copies of the Teichmüller space of hyperbolic metrics with cone singularities of fixed angles. Finally, we use the results on $K$-surfaces to extend to hyperbolic surfaces with cone singularities of angles less than $\pi$ a number of results concerning landslides, which are smoother analogs of earthquakes sharing some of their key properties.References
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Additional Information
- Qiyu Chen
- Affiliation: School of Mathematical Science, Fudan University, 200433, Shanghai, People’s Republic of China
- MR Author ID: 1248105
- Email: chenqy0121@gmail.com
- Jean-Marc Schlenker
- Affiliation: University of Luxembourg, Department of Mathematics, Maison du nombre, 6 avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg
- MR Author ID: 362432
- Email: jean-marc.schlenker@uni.lu
- Received by editor(s): November 21, 2016
- Received by editor(s) in revised form: September 1, 2019
- Published electronically: March 2, 2020
- Additional Notes: The first author was partially supported by NSFC, No. 11771456, and the International Program Funding for Ph.D. Candidates, Sun Yat-Sen University. The author also acknowleges support from Shanghai Postdoctoral Excellence Program (No. 2018018) and China Postdoctoral Science Foundation Grant (No. 2019M661326)
The second author was partially supported by UL IRP grant NeoGeo and FNR grants INTER/ANR/15/11211745 and OPEN/16/11405402. The author also acknowledge support from US National Science Foundation grants DMS-1107452; 1107263; 1107367, “RNMS: GEometric structures And Representation varieties” (the GEAR Network). - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 4013-4049
- MSC (2010): Primary 53C42, 53C50
- DOI: https://doi.org/10.1090/tran/8018
- MathSciNet review: 4105517