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Transactions of the American Mathematical Society

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The spaces of index one minimal surfaces and
stable constant mean curvature surfaces
embedded in flat three manifolds


Authors: Manuel Ritoré and Antonio Ros
Journal: Trans. Amer. Math. Soc. 348 (1996), 391-410
MSC (1991): Primary 53A10; Secondary 49Q20
DOI: https://doi.org/10.1090/S0002-9947-96-01496-1
MathSciNet review: 1322955
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Abstract: It is proved that the spaces of index one minimal surfaces and stable constant mean curvature surfaces with genus greater than one in (non fixed) flat three manifolds are compact in a strong sense: given a sequence of any of the above surfaces we can extract a convergent subsequence of both the surfaces and the ambient manifolds in the $C^k$ topology. These limits preserve the topological type of the surfaces and the affine diffeomorphism class of the ambient manifolds. Some applications to the isoperimetric problem are given.


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Additional Information

Manuel Ritoré
Affiliation: Departamento de Geometría y Topología Universidad de Granada E–18071, Granada, Spain
Email: mritore@ugr.es

Antonio Ros
Affiliation: Departamento de Geometría y Topología Universidad de Granada E–18071, Granada, Spain
Email: aros@ugr.es

DOI: https://doi.org/10.1090/S0002-9947-96-01496-1
Keywords: Minimal surfaces, constant mean curvature surfaces, index one, stability, isoperimetric problem
Received by editor(s): November 18, 1994
Received by editor(s) in revised form: March 27, 1995
Additional Notes: Both authors partially supported by DGICYT grant PB91–0731
Communicated by: Wolmer V. Vasconecelos
Article copyright: © Copyright 1996 American Mathematical Society

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