English

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

R2 v1 2026-06-21T17:24:53.425Z