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Low regularity Poincaré-Einstein metrics


Authors: Eric Bahuaud and John M. Lee
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
Published electronically: December 18, 2017
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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.


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Additional Information

Eric Bahuaud
Affiliation: Department of Mathematics, Seattle University, 901 12th Avenue, Seattle, Washington 98122
Email: bahuaude@seattleu.edu

John M. Lee
Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
Email: johnmlee@uw.edu

DOI: https://doi.org/10.1090/proc/13903
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
Article copyright: © Copyright 2017 American Mathematical Society

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