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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Non-simply connected minimal planar domains in $ \mathbb{H}^2\times\mathbb{R}$


Authors: Francisco Martín and M. Magdalena Rodríguez
Journal: Trans. Amer. Math. Soc. 365 (2013), 6167-6183
MSC (2010): Primary 53A10
Published electronically: March 26, 2013
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Abstract: We prove that any non-simply connected planar domain can be properly and minimally embedded in $ \mathbb{H}^2\times \mathbb{R}$. The examples that we produce are vertical bi-graphs, and they are obtained from the conjugate surface of a Jenkins-Serrin graph.


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Additional Information

Francisco Martín
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, Fuentenueva, 18071, Granada, Spain
Email: fmartin@ugr.es

M. Magdalena Rodríguez
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, Fuentenueva, 18071, Granada, Spain
Email: magdarp@ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05794-7
PII: S 0002-9947(2013)05794-7
Received by editor(s): July 26, 2011
Published electronically: March 26, 2013
Additional Notes: This research was partially supported by MEC-FEDER Grants no. MTM2007 - 61775 and MTM2011 - 22547 and a Regional J. Andalucía Grant no. P09-FQM-5088.
Article copyright: © Copyright 2013 American Mathematical Society