Some rigidity results for asymptotically hyperbolic Einstein metrics

Matthew J. Gursky (University of Notre Dame)    
Some rigidity results for asymptotically hyperbolic Einstein metrics

Abstract
In this talk I will describe some gap estimates for 'even' AHE metrics in dimension four. Even AHE metrics naturally arise from a non-local variational problem, and there is an interesting parallel between uniqueness questions for Einstein metrics on S4 and even AHE metrics on the ball. I will also explain a connection to the study of self-dual AHE metrics. This is joint work with S. McKeown and A. Tyrrell.