Poincar\'e-Einstein metrics and Yamabe invariants
Abstract
In this note we prove the existence of infinitely many positive conformal classes on S7 which cannot be the conformal infinity of a Poincar\'e-Einstein metric on the ball B8. We also prove a sharp inequality between the Yamabe invariant of the conformal infinity and the Yamabe invariant of the interior (after a suitable compactification).
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