Intrinsic characterization of asymptotically hyperbolic metrics and low regularity Poincare-Einstein metrics

Intrinsic characterization of asymptotically hyperbolic metrics and low regularity Poincare-Einstein metrics

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Eric Bahuaud, Seattle University
Fine Hall 401

 A $C^2$ conformally compact Einstein metric has sectional curvature decay to $-1$ up to corrections that are quadratic in the boundary defining function.  In this talk I'll discuss the relationship between curvature decay rate of a generic asymptotically hyperbolic metric and the regularity of the conformal compactification.  I then discuss recent work with John M Lee that proves the existence of a low regularity conformally compact Einstein metric with quadratic hyperbolic curvature decay.