A note on the uniqueness of solutions for the Yamabe problem

Details A note on the uniqueness of solutions for the Yamabe problem A note on the uniqueness of solutions for the Yamabe problem

2011-02-11

arxiv.org/abs/1102.2321v4

Mathematics

Differential Geometry

7 pages. Updated reference list. To appear in Proceedings of the AMS

Scientific paper

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.

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