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Minimal surfaces with
positive genus and finite total curvature in $\mathbb{H}^2
\times \mathbb{R}$
Francisco Martín, Rafe Mazzeo and M Magdalena Rodríguez |
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Geometry & Topology 18 (2014) 141–177
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Abstract |
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We construct the first examples of complete, properly embedded minimal surfaces in with finite total curvature and positive genus. These are constructed by gluing copies of horizontal catenoids or other nondegenerate summands. We also establish that every horizontal catenoid is nondegenerate. |
Keywords
properly embedded minimal surfaces, finite total curvature,
gluing constructions, moduli spaces, minimal surfaces,
positive genus
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Mathematical Subject Classification 2010
Primary: 49Q05, 53A10, 53C42
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References |
Publication
Received: 30 August 2012
Revised: 6 May 2013
Accepted: 19 July 2013
Preview posted: 5 December 2014
Published: 9 January 2014
Proposed: Tobias H Colding
Seconded: David Gabai, Ronald Stern
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Authors |
| Francisco Martín | |
| Departamento de Geometría y
Topología Universidad de Granada 18071 Granada Spain |
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| http://www.ugr.es/local/fmartin | |
| Rafe Mazzeo | |
| Department of Mathematics Stanford University Stanford, CA 94305 USA |
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| http://math.stanford.edu/~mazzeo/ | |
| M Magdalena Rodríguez | |
| Departamento de Geometría y
Topología Universidad de Granada 18071 Granada Spain |
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| http://www.ugr.es/local/magdarp | |
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