Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
MathSciNet review: 1322955
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 53A10, 49Q20

Retrieve articles in all journals with MSC (1991): 53A10, 49Q20


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: http://dx.doi.org/10.1090/S0002-9947-96-01496-1
PII: S 0002-9947(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