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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Graphs and multi-graphs in homogeneous 3-manifolds with isometry groups of dimension 4


Author: Carlos Peñafiel
Journal: Proc. Amer. Math. Soc. 140 (2012), 2465-2478
MSC (2000): Primary 53A35
Published electronically: October 25, 2011
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Abstract: We study the existence of multi-graphs which are immersed in $ E^3(\kappa ,\tau )$, having constant mean curvature $ H$, where $ E^3(\kappa ,\tau )$ is a homogeneous, simply connected 3-manifold whose isometry group has dimension 4.


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Additional Information

Carlos Peñafiel
Affiliation: Instituto de Matemática, Universidade Federal de Rio de Janeiro, Rio de Janeiro, 22453-900, Brazil
Email: penafiel@im.ufrj.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11075-X
PII: S 0002-9939(2011)11075-X
Keywords: Constant mean curvature, graphs and multi-graphs, homogeneous 3-manifolds
Received by editor(s): July 29, 2010
Received by editor(s) in revised form: February 14, 2011
Published electronically: October 25, 2011
Additional Notes: The author was supported by FAPER, Brazil
Communicated by: Jianguo Cao
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.