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.References
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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
- MR Author ID: 601604
- 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
- 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
- © Copyright 2012 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 4351-4357
- MSC (2010): Primary 53C25, 58E11
- DOI: https://doi.org/10.1090/S0002-9939-2012-11284-5
- MathSciNet review: 2957225