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arXiv · 1702.00294

Poincar\'e-Einstein metrics and Yamabe invariants

Matthew J. Gursky·Qing Han
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Abstract

In this note we prove the existence of infinitely many positive conformal classes on $S^7$ which cannot be the conformal infinity of a Poincar\'e-Einstein metric on the ball $B^8$. 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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Matthew J. Gursky, Qing Han. 2017-02-01. Poincar\'e-Einstein metrics and Yamabe invariants. https://arxiv.org/abs/1702.00294

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