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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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