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

 

Stable hypersurfaces with constant scalar curvature


Authors: Hilário Alencar, Walcy Santos and Detang Zhou
Journal: Proc. Amer. Math. Soc. 138 (2010), 3301-3312
MSC (2010): Primary 53C42
Published electronically: April 22, 2010
MathSciNet review: 2653960
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Abstract: We obtain some nonexistence results for complete noncompact stable hypersurfaces with nonnegative constant scalar curvature in Euclidean spaces. As a special case we prove that there is no complete noncompact strongly stable hypersurface $ M$ in $ \mathbb{R}^{4}$ with zero scalar curvature $ S_2$, nonzero Gauss-Kronecker curvature and finite total curvature (i.e. $ \int_M\vert A\vert^3<+\infty$).


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Additional Information

Hilário Alencar
Affiliation: Instituto de Matemática, Universidade Federal de Alagoas, 57072-900 Maceió-AL, Brazil
Email: hilario@mat.ufal.br

Walcy Santos
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21941-909, Rio de Janeiro-RJ, Brazil
Email: walcy@im.ufrj.br

Detang Zhou
Affiliation: Instituto de Matemática, Universidade Federal Fluminense, 24020-140, Niterói-RJ, Brazil
Email: zhou@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10388-8
PII: S 0002-9939(10)10388-8
Received by editor(s): September 10, 2009
Received by editor(s) in revised form: December 25, 2009
Published electronically: April 22, 2010
Additional Notes: The authors were partially supported by CNPq and FAPERJ, Brazil.
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.