English

Poincar\'e-Einstein metrics and Yamabe invariants

Differential Geometry 2017-02-02 v1

Abstract

In this note we prove the existence of infinitely many positive conformal classes on S7S^7 which cannot be the conformal infinity of a Poincar\'e-Einstein metric on the ball B8B^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).

Keywords

Cite

@article{arxiv.1702.00294,
  title  = {Poincar\'e-Einstein metrics and Yamabe invariants},
  author = {Matthew J. Gursky and Qing Han},
  journal= {arXiv preprint arXiv:1702.00294},
  year   = {2017}
}
R2 v1 2026-06-22T18:06:45.407Z