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On stable compact minimal submanifolds


Authors: Francisco Torralbo and Francisco Urbano
Journal: Proc. Amer. Math. Soc. 142 (2014), 651-658
MSC (2010): Primary 53C40, 53C42
DOI: https://doi.org/10.1090/S0002-9939-2013-11810-1
Published electronically: October 25, 2013
MathSciNet review: 3134005
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Abstract: Stable compact minimal submanifolds of the product of a sphere and any Riemannian manifold are classified whenever the dimension of the sphere is at least three. The complete classification of the stable compact minimal submanifolds of the product of two spheres is obtained. Also, it is proved that the only stable compact minimal surfaces of the product of a $ 2$-sphere and any Riemann surface are the complex ones.


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Additional Information

Francisco Torralbo
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email: ftorralbo@ugr.es

Francisco Urbano
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email: furbano@ugr.es

DOI: https://doi.org/10.1090/S0002-9939-2013-11810-1
Keywords: Stability, minimal submanifolds, product spaces, spheres
Received by editor(s): December 3, 2010
Received by editor(s) in revised form: March 20, 2012
Published electronically: October 25, 2013
Additional Notes: This research was partially supported by MEyC-Feder research projects MTM2007-61775, MTM2011-22547 and the Junta Andalucía Grants P06-FQM-01642 and P09-FQM-4496.
Communicated by: Michael Wolf
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.