Some existence and non-existence results for Poincare-Einstein metrics

Some existence and non-existence results for Poincare-Einstein metrics

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Matthew Gursky, University of Notre Dame
Rutgers - Hill Center, Room 705

I will begin with a brief overview of the existence question for conformally compact Einstein manifolds with prescribed conformal infinity.   After stating the seminal result of Graham-Lee, I will discuss a non-existence result (joint with Qing Han) for certain conformal classes on the 7-dimensional sphere.  I will also mention some ongoing work (with Gabor Szekelyhidi) on a version of "local existence" of Poincare-Einstein metrics.