Low regularity Poincaré-Einstein metrics

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.

14 pages

References in corpus (1)

• Rigidity of Asymptotically Hyperboblic Manifolds