A note on the uniqueness of solutions for the Yamabe problem
Differential Geometry
2011-06-10 v4
Abstract
We prove that in conformal classes of metrics near the class of an Einstein metric (other than the standard round metric on a sphere) the Yamabe problem has a unique solution up to scaling. This is a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.
Keywords
Cite
@article{arxiv.1102.2321,
title = {A note on the uniqueness of solutions for the Yamabe problem},
author = {L. L. de Lima and P. Piccione and M. Zedda},
journal= {arXiv preprint arXiv:1102.2321},
year = {2011}
}
Comments
7 pages. Updated reference list. To appear in Proceedings of the AMS