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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the uniqueness of solutions for the Yamabe problem


Authors: L. L. de Lima, P. Piccione and M. Zedda
Journal: Proc. Amer. Math. Soc. 140 (2012), 4351-4357
MSC (2010): Primary 53C25, 58E11
Published electronically: April 20, 2012
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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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Additional Information

L. L. de Lima
Affiliation: Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, 60455-760, Brazil

P. Piccione
Affiliation: Departamento de Matemática, Universidade de São Paulo, São Paulo, 05508-090, Brazil

M. Zedda
Affiliation: Università degli Studi di Cagliari, Via Università 240, 09124 Cagliari, Italy
Address at time of publication: Departamento de Matemática, Universidade de São Paulo, São Paulo, 05508-090, Brazil

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11284-5
PII: S 0002-9939(2012)11284-5
Received by editor(s): February 11, 2011
Received by editor(s) in revised form: February 15, 2011, and June 2, 2011
Published electronically: April 20, 2012
Additional Notes: The first author is partially sponsored by CNPq and Funcap, Brazil.
The second author is partially sponsored by CNPq and Fapesp, Brazil.
The third author is supported by RAS through a grant financed with the “Sardinia PO FSE 2007-2013” funds and provided according to the L.R. 7/2007.
Communicated by: Jianguo Cao
Article copyright: © Copyright 2012 American Mathematical Society