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
Posted:
August 24, 2011
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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.
References
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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
PII:
S 0002-9939(2011)11197-3
Keywords:
Stable surfaces,
bifurcation
Received by editor(s):
August 2, 2010
Received by editor(s) in revised form:
January 14, 2011
Posted:
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
