Low regularity Poincaré-Einstein metrics

Published 5 Jan 2017 in math.DG and math.AP | (1701.01481v2)

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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