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Rigidity of stable cylinders in three-manifolds


Author: José M. Espinar
Journal: Proc. Amer. Math. Soc. 140 (2012), 1769-1775
MSC (2010): Primary 53A10; Secondary 53C24, 49Q05
DOI: https://doi.org/10.1090/S0002-9939-2011-11197-3
Published electronically: August 24, 2011
MathSciNet review: 2869162
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Abstract: In this paper we show how the existence of a certain stable cylinder determines (locally) the ambient manifold where it is immersed. This cylinder has to verify a bifurcation phenomenon; we make this explicit in the introduction. In particular, the existence of such a stable cylinder implies that the ambient manifold has infinite volume.


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Additional Information

José M. Espinar
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email: jespinar@ugr.es

DOI: https://doi.org/10.1090/S0002-9939-2011-11197-3
Keywords: Stable surfaces, bifurcation
Received by editor(s): August 2, 2010
Received by editor(s) in revised form: January 14, 2011
Published electronically: August 24, 2011
Additional Notes: The author is partially supported by the Spanish MEC-FEDER Grant MTM2010-19821 and Regional J. Andalucia Grants P06-FQM-01642 and FQM325.
Communicated by: Michael Wolf
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.