A note on the uniqueness of solutions for the Yamabe problem

de Lima, L.; Piccione, P.; Zedda, M.

doi:10.1090/S0002-9939-2012-11284-5

A note on the uniqueness of solutions for the Yamabe problem
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by L. L. de Lima, P. Piccione and M. Zedda PDF

Proc. Amer. Math. Soc. 140 (2012), 4351-4357 Request permission

Abstract:

Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.

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