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 which cannot be the conformal infinity of a Poincar\'e-Einstein metric on the ball . 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}
}