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A Costa-Hoffman-Meeks type surface in $ {\mathbb{H}^2 \times \mathbb{R} }$


Author: Filippo Morabito
Journal: Trans. Amer. Math. Soc. 363 (2011), 1-36
MSC (2000): Primary 53A10, 49Q05
DOI: https://doi.org/10.1090/S0002-9947-2010-04952-9
Published electronically: September 1, 2010
MathSciNet review: 2719669
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Abstract: We show the existence in the space $ {\mathbb{H}}^2 \times \mathbb{R}$ of a family of embedded minimal surfaces of genus $ 1\leqslant k<+\infty$ and finite total extrinsic curvature with two catenoidal type ends and one middle planar end. The proof is based on a gluing procedure.


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Additional Information

Filippo Morabito
Affiliation: Laboratoire d’Analyse et Mathématiques Appliquées, Université Paris-Est, CNRS UMR 8050, 5 blvd Descartes, 77454 Champs-sur-Marne, France – and – Dipartimento di Matematica, Università Roma Tre, Largo S. L. Murialdo 1, 00146 Roma, Italy
Address at time of publication: School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongnyangni 2-Dong, Dongdaemun-gu Seoul 130-722, Korea
Email: morabito@mat.uniroma3.it, filippo.morabito@univ-mlv.fr

DOI: https://doi.org/10.1090/S0002-9947-2010-04952-9
Received by editor(s): April 4, 2008
Published electronically: September 1, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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