Low regularity Poincaré–Einstein metrics
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- by Eric Bahuaud and John M. Lee PDF
- Proc. Amer. Math. Soc. 146 (2018), 2239-2252 Request permission
Abstract:
We prove the existence of a $C^{1,1}$ conformally compact Einstein metric on the ball that has asymptotic sectional curvature decay to $-1$ plus terms of order $e^{-2r}$ where $r$ is the distance from any fixed compact set. This metric has no $C^2$ conformal compactification.References
Additional Information
- Eric Bahuaud
- Affiliation: Department of Mathematics, Seattle University, 901 12th Avenue, Seattle, Washington 98122
- MR Author ID: 854286
- ORCID: 0000-0002-6383-7487
- Email: bahuaude@seattleu.edu
- John M. Lee
- Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
- MR Author ID: 203084
- Email: johnmlee@uw.edu
- Received by editor(s): February 19, 2017
- Received by editor(s) in revised form: July 16, 2017
- Published electronically: December 18, 2017
- Additional Notes: This work was supported by a grant from the Simons Foundation (#426628, Eric Bahuaud)
- Communicated by: Guofang Wei
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2239-2252
- MSC (2010): Primary 53C21; Secondary 35B65, 35J57, 35J70, 53C25
- DOI: https://doi.org/10.1090/proc/13903
- MathSciNet review: 3767374