Transactions of the American Mathematical Society

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

Author(s): Manuel Ritoré; Antonio Ros
Journal: Trans. Amer. Math. Soc. 348 (1996), 391-410.
MSC (1991): Primary 53A10; Secondary 49Q20
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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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Manuel Ritoré
Affiliation: Departamento de Geometría y Topología Universidad de Granada E--18071, Granada, Spain
Email: mritore@ugr.es

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