A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

作者：de Lima L L^*; Piccione P; Zedda M

来源：Proceedings of the American Mathematical Society, 2012, 140(12): 4351-4357.

DOI：10.1090/S0002-9939-2012-11284-5

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.

• 出版日期2012-12