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.
A note on the uniqueness of solutions for the Yamabe problem / DE LIMA, LEVI LOPES; Piccione, Paolo; Zedda, Michela. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 140:(2012), pp. 4351-4357. [10.1090/S0002-9939-2012-11284-5]
A note on the uniqueness of solutions for the Yamabe problem
ZEDDA, MICHELA
2012-01-01
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.File in questo prodotto:
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