Poincaré-Einstein metrics and Yamabe invariants

2017/02/01 by Gursky, Matthew J., Han, Qing
#53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.00294

Abstract

In this note we prove the existence of infinitely many positive conformal classes on S⁷ which cannot be the conformal infinity of a Poincaré-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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