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

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:
http://dx.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.